
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
Given a triangle \( ABC \) with the longest side \( BC \). The bisector of angle \( C \) intersects the altitudes \( AA_1 \) and \( BB_1 \) at points \( P \) and \( Q \) respectively, and the circumcircle of \( ABC \) at point \( L \). Find \(\angle ACB\), given that \( AP = LQ \).

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