"Мы собираемся пойти в кино. Хочешь с нами?"
Translation:We are going to the cinema. Do you want to come with us?
"We are planning to go to the movies. Do you want to go with us?" seems like it should work.
I agree. The verb used in the orevious sentence is go. The second sentence does not have a motion verb. The verb from the orevious sentence us implied.
Why is “We are going to the cinema” correct and not just “We are going to go to the cinema”? I thought собираемся accounts for the future and пойти is the actual action that takes place in the future—in contrast, “going to the cinema” makes no assertion about the action taking place in the future. Instead, it's a present continuous.
In both American and British English, it's common to leave out the second go (or to merge both of them), the future tense will be implied on the sentence. But I do think going to go is correct.