
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 touches the sides of an angle at points \( A \) and \( B \). The distance from a point \( C \) lying on the circle to the line \( AB \) is 6. Find the sum of the distances from point \( C \) to the sides of the angle, given that one of these distances is nine times less than the other.

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