
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, one centered at $A$ with a radius of $2$ units and another centered at $B$ with a radius of $3$ units, are externally tangent to each other. A third circle is tangent to both of these circles and also to one of their common external tangents. Determine the radius of the third circle.

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