
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
The side lengths of a right triangle are integers, with no common divisor greater than 1. The radius of the circle tangent to the hypotenuse is 420 units. Determine the side lengths.

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