inter- prefix means between but interact has a whole different meaning than -inter or act, why is that?

I just started to dig into suffixes and prefixes. But I couldn't understand how do they exactly change the meaning of the word that they are appended.

For example re- means again, retake means take again. Inter- means between, but interact means acting in a way that you have an effect on something. Interact has no connection with between. Why is that?

Solution 1:

Inter- has the following definitions:

1. Between; among.
   ‘inter-agency’, ‘interblend’
2. Mutually; reciprocally.
   ‘interactive’

The between is the fourth definition:

Indicating a connection or relationship involving two or more parties.

According to Etymonline, interact means:

"act on each other, act reciprocally," 1805, from inter- + act (v.).

In addition, Lexico defines it thus:

1. Act in such a way as to have an effect on each other.