
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 triangle \( ABC \), angle \( A \) is a right angle and angle \( B \) is \( 30^\circ \). A circle of radius \(\sqrt{3}\) is inscribed in the triangle.

Find the distance from vertex \( C \) to the point of tangency of this circle with the leg \( AB \).

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