
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
From a common point, two tangents are drawn to a circle. The radius of the circle is 11, and the sum of the lengths of the tangents is 120.

Find the distance from the center of the circle to the common point of tangency.

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