
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 right triangle $ABC$, where $\overline{BC} = 3$ and $\overline{AC} = a$, a second right triangle $ABD$ is constructed such that $AB$ is the hypotenuse for both triangles and $\overline{AD} = 4$. Determine $\overline{BD}$.
A) \(\sqrt{a^2-5}\)
B) \(\sqrt{a^2-7}\)
C) \(a^2-7\)
D) \(\sqrt{a^2-9}\)
E) \(\sqrt{a^2-11}\)

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