
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
Inside triangle \(ABC\) there are three circles \(k_1, k_2, k_3\), each of which is tangent to two sides of the triangle and to its incircle \(k\). The radii of \(k_1, k_2, k_3\) are 1, 4, and 9. Determine the radius of \(k\).

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