
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 10 respectively. A circle is drawn with one focus of the ellipse as its center, such that the circle is tangent to the ellipse with no part outside the ellipse. Determine the circle's radius.

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