
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 a quadrilateral $ABCD$ with right angles at $A$ and $C$, points $E$ and $F$ are located on line segment $\overline{AC}$ such that lines $\overline{DE}$ and $\overline{BF}$ are perpendicular to $\overline{AC}$. Given $AE=4$, $DE=6$, and $CE=7$, find the length of $BF$.

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