
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
Consider two circles, one centered at $A$ with radius $2$ and another centered at $B$ with radius $5$. These two circles are externally tangent. There is a third circle that is tangent to both these circles and to one of their common external tangents. Find the radius of this third circle.

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