Add an action to Moderator Logs?

[Irishnotsane]

So long story short, we have a mod that allows moderators to click a red tick which is below each post, which clicked, turns the tick green to effectively tell other moderators that this post has been checked (ticking post #23 for example.. also marks all previous posts in that thread as marked too, with a green tick) so if there are 50 posts in a thread. Ticking the last post essentially marks the whole thread with a green tick.

How do we go about adding said action to the moderators log?
So that it'll display in the logs when said users have clicked the red tick?