
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
In the right triangle \(ABC\), the leg \(AB = 3\), and the leg \(AC = 6\). The centers of circles with radii 1, 2, and 3 are located at points \(A\), \(B\), and \(C\) respectively. Find the radius of the circle that is externally tangent to each of these three given circles.

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