
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a planar setup, a regular pentagon with side length $s$ contains a circle that is tangent to two non-adjacent sides of the pentagon while intersecting two other sides. The circle is tangent at points $P$ and $Q$ around the corner $C$ of the pentagon. Let the center of the pentagon be $O$. Calculate the degree measure of $\angle POQ$ given each internal angle of the pentagon is $108^\circ$ and the line $OP$ bisects $\angle CPQ$.

Present the answer in LaTex format: \boxed{Your answer}
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