
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 incircle  $\Gamma$  of a scalene triangle  $ABC$  touches  $BC$  at  $D, CA$  at  $E$  and  $AB$  at  $F$ . Let  $r_A$  be the radius of the circle inside  $ABC$  which is tangent to  $\Gamma$  and the sides  $AB$  and  $AC$ . Define  $r_B$  and  $r_C$  similarly. If  $r_A = 16, r_B = 25$  and  $r_C = 36$ , determine the radius of  $\Gamma$ .

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