
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 acute triangle \(ABC\), the altitudes \(AA_1\) and \(BB_1\) are drawn. The bisector of the exterior angle at vertex \(C\) intersects lines \(AB\) and \(A_1B_1\) at points \(L\) and \(K\) respectively. It turns out that \(CL = 2CK\). Find the angle \(C\).

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