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Shabbos Mevarchim Tishrei:
Tehillim: The entire book of Tehillim is recited before Shacharis just as on any other Shabbos Mevarchim.
Farbrengen: At the conclusion of the prayers one is to have a Chassidic gathering as is done on every Shabbos Mevarchim. This gathering is to include good and practical resolutions in matters of spiritual and physical charity.
Omitting Vayehi Noam: The entire prayer of Vayehi Noam is customarily omitted on the Motzei Shabbos directly prior to any Holiday including Rosh Hashanah. If however Rosh Hashanah falls on Shabbos, Vayehi Noam is recited the previous Motzei Shabbos.
Sparks of Chassidus
Hashem blesses this month:
On the Shabbos before Rosh Hashanah, which is the last Shabbos of the month of Elul, we read the passage in the Torah which begins נצבים אתם. These words are G-d’s blessing to the Jewish people. The Rebbe Rayatz records the following statement from his father the Rebbe Rashab: When I was a child I asked my father, the Rebbe Maharash, “Why do we not bless the month of Tishrei as we bless the other months?” The Rebbe Maharash in turn replied that when he was a child he had asked the same question to his father the Tzemach Tzedek who in turn said that when he was a child he asked this question to his grandfather the Alter Rebbe. The Alter Rebbe replied that he heard the following teaching in Mezritch from his master, the Maggid, who had received it from his master, the Baal Shem Tov: The seventh month [i.e. Tishrei], which is the first of the months of the year, is blessed by G-d Himself on Shabbos Mevarchim, which is the last Shabbos of the month of Elul. By virtue of this blessing the Jews are empowered to bless the other months eleven times a year. This is the content of G-d’s blessing: “Atem Nitzavim Hayom” [i.e. You are standing this day]. The word היום [i.e. this day] refers to Rosh Hashanah, which is the Day of Judgment. The phrase Atem Netzavim implies not only that the Jewish people are standing, but furthermore that on this day “you are sustained in your firm stance” which means that you are acquitted in your trial.
 Drasha of Rav: Some Poskim write the Rav is to give a speech on the Shabbos before R”H in order to arouse the people in repentance. This has support in the Midrash which states that when the Sage expounds the laws to the public Hashem forgives their sins. [Mateh Moshe 833; Kneses Hagedola 602/4; Elya Raba 603/2; Kaf Hachaim 602/10]
 Magen Avraham 417/1; Levush 421/1; 581/1; Mateh Efraim 581/47
 The reason: The reason for this is because the verse in Psalms states on Rosh Chodesh “Bikese Leyom Chageinu” which implies that Rosh Hashanah is to be concealed. Hence we do not announce the date of Rosh Chodesh which is the date of Rosh Hashanah. [Magen Avraham ibid] The reason we desire to conceal Rosh Hashanah is in order to confuse the Satan and prevent him from prosecuting against us on that day. [Levush 421/1]. The Rebbe explains that the Satan is confused by the lack of mentioning Rosh Chodesh as he now becomes even more convinced that the Jews are positive that their judgment has been sealed for good, and it is for this reason that they are not doing the Mitzvah of Rosh Chodesh. This hence weakens the Satans prosecution, being that he suspects that perhaps the judgment has already been secured. It also diminishes the Satans personal prosecutions as he sees that they are lacking the merit of Rosh Chodesh and hence a strong prosecution is not that necessary. Nevertheless in truth the above explanation does not suffice to justify annulling a custom of Jewry as practically we are now lacking the Avoda of Rosh Chodesh. Thus in truth the intent of not mentioning Rosh Chodesh is to arouse one in Teshuvah, so we become broken over the Mitzvah that was removed from us. It is this Teshuvah that is done due to feeling broken hearted that capsizes the Satans prosecution.[Likkutei Sichos 24 printed in Shaar Hamoadim Rosh Hashanah 5]
The Chassidic reason: See Sparks of Chassidus!
 Sefer Haminhagim p. 115 [English Edition]; Takanos of Rebbe Rayatz printed in Otzer Minhagei Chabad 81
 Mateh Efraim 581/47; Shaareiy Efraim 10/35; Toras Menachem 1990 4/299 [Sichas Netzavim Vayeilech; brought in Shaareiy Halacha Uminhag 5/68; Shulchan Menachem 3/75]
 The reason: Although on a regular Shabbos Mivarchim the paragraph of Av Harachamim is omitted, nevertheless since on this Shabbos the month is not verbally blessed in Shul therefore one is to recite this paragraph.
 This especially applies when this Shabbos is also Shabbos Selichos of which Chassidim were always accustomed to have a Farbrengen on this Shabbos. [See Hisvadyus 1951 2/327; 1982 4/2253; 1983 4/2045]
 Hisvadyos 1988 4/376
 295/3 regarding every Yom Tov; Mateh Efraim 581/47; See “The Laws and Customs of Motzei Shabbos” chapter 1 Halacha 4 further details on this subject!
 This includes also the prayer of Ata Kadosh. The reason it is accustomed to omit also Ata Kadosh is because the prayer of Ata Kadosh is said as a result of saying the prayer of Vayehi Noam. As once the Shechina resides below, as is stated in the prayer of Vayehi Noam which discusses the Mishkan, it is then fit to sanctify it with the prayer of Ata Kadosh. Thus since Vayehi Noam is omitted, [for the reason to be explained in the next footnote] so too we omit Ata Kadosh. [ibid]
Other Opinions: The above follows the Ashkenazi custom, as brought by the Tur. However the Sefardi custom is to only omit Vayehi Noam and Yosheiv Beseiser and they begin from Orech Yamim, and then say Ata Kadosh. [Tur] Some however say the Sefaradi custom is to recite it entirely, as rule the Sefaradi sources brought in the next footnote. [Piskeiy Teshuvos 294/2]
 The reason: The reason for omitting Vayehi Noam is because within the prayer we say twice “And the work of our hands”, hence all the days of the coming week have to be fit for work. If they are not all fit for work then we simply omit the prayer. [ibid; See Piskeiy Teshuvos 294/2 for a thorough analyses on this subject]
Other Opinions: Some, based on Kabala of Arizal, always recite the prayer of Vayehi Noam on Motzei Shabbos, even when a Holiday falls that week, and even on Motzei Shabbos Chol Hamoed. Nevertheless in such circumstances they recite it quietly. Their reasoning is because Vayehi Noam affects the influence of Shabbos on the weekday which is needed every week, without exception. [Birkeiy Yosef brought in Shaareiy Teshuvah 295/2; Kaf Hachaim 295/9-10]
 So rules Admur ibid regarding all Holidays; M”E ibid regarding Rosh Hashanah; M”E 602/45 regarding Shabbos Shuva; See Otzer Minhagei Chabad p. 170 for difference in practice of the Rebbe over the years by Shabbos Teshuvah
Other Opinions: Some rule that even in such a case that Yom Tov falls on Shabbos, Vayehi Noam is omitted the Motzei Shabbos prior to it. [See Kaf Hachaim 295/6]
 Hayom Yom 25th Elul; Sefer Haminhagim p. 115 [English]