
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
Sean \( D, E, F \) los puntos de tangencia del círculo inscrito al triángulo \( ABC \) con los lados \( BC, AC \) y \( AB \) respectivamente. Demuestra que

\[ 4 S_{DEF} \leq S_{ABC} \]

donde \( S_{XYZ} \) denota el área del triángulo \( XYZ \).

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