
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 $\triangle ABC$, where $\angle BAC = 90^\circ$, points $D$ and $E$ are on the hypotenuse $BC$ such that $CD = CA$ and $BE = BA$. Point $F$ is inside $\triangle ABC$ such that $\triangle DEF$ is an isosceles right triangle with $DE$ as the hypotenuse. Find $\angle BFC$.

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