
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 the quadrilateral $ABCD$, where points $A$, $B$, $C$, and $D$ form the vertices with right angles at $A$ ($\angle BAC$) and at $C$ ($\angle BCD$). On side $\overline{AC}$, points $E$ and $F$ fall on it, such that both $\overline{DF}$ and $\overline{BE}$ are perpendicular to $\overline{AC}$. Given that $AF = 4$, $DF = 6$, and $CF = 8$, find $BE$.

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