
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 hyperbola is drawn with transverse and conjugate axes of lengths 12 and 10 respectively. Using one focus as a center, a circle is drawn that is tangent to the hyperbola, with no part of the circle being outside the hyperbola. Compute the radius of the circle.

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