Another interpretation: "I am the LORD your God" - when the Holy One, blessed be He, stood and said "I am the LORD your God," the mountains and hills were quaking, and Tabor and Hermon came from Beit Elim, and Carmel from Aspamia, as it says "As I live, says the King, the LORD of hosts is His name, surely like Tabor among the mountains" and so on (Jeremiah 46:18). This one says, I have been chosen, and that one says, I have been chosen. But once they heard from Your mouth "who brought you out of the land of Egypt," each one stood in its place, and said, He concerned Himself only with the one He brought out of Egypt.
Mountains Rush to Sinai Each Claiming the Revelation
Yalkut Shimoni on Torah 286:8
דָּבָר אַחֵר אָנֹכִי ה' אֱלֹהֶיךָ, כְּשֶׁעָמַד הַקָּדוֹשׁ בָּרוּךְ הוּא וְאָמַר אָנֹכִי ה' אֱלֹהֶיךָ, הָיוּ הֶהָרִים וְהַגְּבָעוֹת מִתְרַגְּשִׁין, וּבָא תָּבוֹר וְחֶרְמוֹן מִבֵּית אֵלִים, וְכַרְמֶל מֵאַסְּפַּנְיָא, שֶׁנֶּאֱמַר (ירמיה מו, יח) "חַי אֲנִי נְאֻם הַמֶּלֶךְ ה' צְבָאוֹת שְׁמוֹ כִּי כְּתָבוֹר בֶּהָרִים" וְגוֹ'. זֶה אוֹמֵר אֲנִי נִקְרֵאתִי, וְזֶה אוֹמֵר אֲנִי נִקְרֵאתִי, וְכֵיוָן שֶׁשָּׁמְעוּ מִפִּיךָ אֲשֶׁר הוֹצֵאתִיךָ מֵאֶרֶץ מִצְרַיִם, עָמַד כָּל אֶחָד וְאֶחָד בִּמְקוֹמוֹ, וְאָמַר לֹא עָסַק אֶלָּא עִם מִי שֶׁהוֹצִיא מִמִּצְרַיִם.