
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 its major and minor axes of lengths 12 and 6 respectively. A circle is drawn using one of the foci of the ellipse as its center, such that it is tangent to the ellipse without extending outside of it. Determine the radius of this circle.

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