
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 circle $\omega$ is circumscribed around triangle $ABC$. A line tangent to $\omega$ at point $C$ intersects ray $BA$ at point $P$. On ray $PC$ beyond point $C$, a point $Q$ is marked such that $PC = QC$. Segment $BQ$ intersects circle $\omega$ again at point $K$. On the smaller arc $BK$ of circle $\omega$, a point $L$ is marked such that $\angle LAK = \angle CQB$. Find the angle $\angle PCA$ given that $\angle ALQ = 60^\circ$.

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