
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 sector $OAB$ with a central angle of $90^{\circ}$, a point $P$ moves along the arc $\overparen{A B}$ (excluding the endpoints $A$ and $B$). The line $PQ$ is tangent to the arc $\overparen{A B}$ and intersects the line $OA$ at point $Q$. Identify the locus of the incenter $I$ of triangle $\triangle OPQ$ and provide a justification.

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