
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
A quadrilateral \(ABCD\) is inscribed in a circle \(\omega\) whose center lies on side \(AB\). Circle \(\omega_1\) is externally tangent to circle \(\omega\) at point \(C\). Circle \(\omega_2\) is tangent to circles \(\omega\) and \(\omega_1\) at points \(D\) and \(E\) respectively. Line \(BD\) intersects circle \(\omega_2\) again at point \(P\), and line \(AC\) intersects circle \(\omega_1\) again at point \(Q\). Find the angle \(PEQ\).

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