
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 the hypotenuse $AB$ of right triangle $ABC$ a second right triangle $ABD$ is constructed with hypotenuse $AB$. If $BC = 2$, $AC = c$, and $AD = c-1$, find the length $\overline{BD}$.
A) $\sqrt{c+2}$
B) $\sqrt{6c-3}$
C) $\sqrt{3 + 2c}$
D) $c + 1$

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