True or false, the government pushing a company to censor free speech is illegal?

Notice I said "government". It's absolutely fine for a private company to censor speech on their platforms, save for when it's the government pushing them to do it, that is when it violates the constitution. The government has zero rights to censor, or push others to censor speech.
True
False because I failed to take a civics class, or failed to read the word government in the post.
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True or false, the government pushing a company to censor free speech is illegal?
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