
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 the right triangle \(ABC\) with the right angle at \(C\), points \(P\) and \(Q\) are the midpoints of the angle bisectors drawn from vertices \(A\) and \(B\). The circle inscribed in the triangle touches the hypotenuse at point \(H\). Find the angle \(PHQ\).

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