
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
Let  $ABC$  be an acute triangle and  $AD$  a height. The angle bissector of  $\angle DAC$  intersects  $DC$  at  $E$ . Let  $F$  be a point on  $AE$  such that  $BF$  is perpendicular to  $AE$ . If  $\angle BAE=45º$ , find  $\angle BFC$ .

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