
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 $ABC$, $\angle C = 90^\circ$, $AC = 5$ and $BC = 12$. Point $D$ is on $\overline{AB}$, point $E$ is on $\overline{BC}$, and point $F$ is on $\overline{AC}$ such that $\angle FED = 90^\circ$. If $DE = 5$ and $DF = 3$, then what is the length of $BD$?

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