
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
Two circles are centered at points \( A \) and \( B \) respectively with radii 2 and 5. These circles are externally tangent to each other. A third circle is tangent to the first two circles and also tangent to one of their common external tangents. Determine the radius of the third circle.

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