Movement towards action refers to sentences like the following:

I am going to eat.
I am coming to meet her.
I went to watch a football game.

In Japanese we use the following structure.

【Verb: Stem】く】or【る】
To go/come to do something
いにます。
To come and meet.
明日あしたは、銀座ぎんざ寿司すしべにきます。
Tomorrow I’m going to go and eat sushi in Ginza [a place in Tokyo].
あそびにませんか?
Won’t you come and hang out.
サーカーの試合しあいきました。
I went to watch a football game.

It is easy to slip up on the grammar here. You might think that to say “I will go to study in the library” (for example) the grammar should be…

図書館としょかん勉強べんきょうしにきます。()
I went to watch a football game.

… because the library is the place of action and the following, as we have seen, is correct:

図書館としょかん勉強べんきょうします。
I will study in the library.

However, when we want to express movement towards an action it is the final verb—“to go” or “to come”—which dictates the particle and therefore we must use に.

図書館としょかん勉強べんきょうしにきます。
I will go to study in the library.

We need to be careful when using the directional particle.

東京駅とうきょうえききます。()
東京駅とうきょうえききます。()
I will go to Tokyo station.

That’s fine. But the directional particle cannot be used to join the two verbs.

銀座ぎんざ寿司すしきます。()
銀座ぎんざ寿司すしべにきます。()
I will go to eat sushi in Ginza.
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