
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 to each other; the first circle is centered at \(A\) with a radius of \(2\), and the second circle is centered at \(B\) with a radius of \(3\). A third circle is tangent to both these circles and one of the common external tangents of the first two circles. Find the radius of the third circle.

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