
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 an acute triangle \( ABC \), the altitudes \( AA_1 \), \( BB_1 \), and \( CC_1 \) are drawn. A point \( T \) is chosen on the plane such that the lines \( TA \) and \( TB \) are tangents to the circumcircle of triangle \( ABC \). Let \( O \) be the center of this circumcircle. A perpendicular dropped from point \( T \) to line \( A_1B_1 \) intersects line \( CC_1 \) at point \( K \), and the line passing through point \( C_1 \) parallel to \( OK \) intersects segment \( CO \) at point \( L \). Find the angle \( \angle CLA_1 \).

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