Have you discussed this with your DM? Why don't you 'attack' this problem at its root, instead of silently suffering through it?Because sometimes other people's turns go like this.
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In our game we also have/had this kind of player which is why we started using an hour-glass. I.e. every player (including the DM) has one minute to formulate his actions; if time runs out without him or her making a decision, the pc either takes a default action (definable by the player) or delays.
We expect players to be ready when their turn comes up. I guess that alone makes sure opportunities for getting bored are greatly reduced.