
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 externally tangent, one centered at $P$ with a radius of $2$ and another at $Q$ with a radius of $5$. A third circle is externally tangent to the first two circles and 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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