
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
Given three circles with radii 1, 2, and 3, respectively, each pair touching each other externally at points \(A\), \(B\), and \(C\). Find the radius of the inscribed circle of triangle \(ABC\).

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