
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 triangle \(ABC\), point \(D\) is taken on side \(AC\) such that the circles inscribed in triangles \(ABD\) and \(BCD\) are tangent to each other. It is known that \(AD = 2\), \(CD = 4\), and \(BD = 5\). Find the radii of the circles.

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