
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
Given that  $ABCD$  is a quadrilateral with right angles at  $A$  and  $C$ , points  $E$  and  $F$  are on  $AC$ , and  $DE$  and  $BF$  are perpendicular to  $AC$ . If  $AE=3$ ,  $DE=5$ , and  $CE=7$ , calculate  $BF$.

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