
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
An ellipse has major and minor axes of lengths 12 and 6, respectively. Using one focus as the center, a circle is drawn such that it is tangent to the ellipse with no part of the circle outside the ellipse. Compute the radius of the circle.

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