
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 $ABC$, a second right triangle $ABD$ is constructed with hypotenuse $AB$. If $\overline{BC}=3$, $\overline{AC}=a$, and $\overline{AD}=4$, compute $\overline{BD}$.
A) $\sqrt{a^2 + 7}$
B) $\sqrt{a^2 - 7}$
C) $\sqrt{a^2 + 9}$
D) $\sqrt{a^2 - 9}$
E) $\sqrt{a^2 + 12}$

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