
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
On hypotenuse $AB$ of a right triangle $ABC$, another right triangle $ABD$ is constructed with $AB$ also as its hypotenuse. If $\overline{BC} = 3$, $\overline{AC} = c$, and $\overline{AD} = 4$, find $\overline{BD}$.
A) $\sqrt{c^2 + 3}$
B) $c^2 - 4$
C) $\sqrt{c^2 - 7}$
D) $c^2 + 9$
E) $\sqrt{c^2 + 9}$

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