
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
Consider all triangles $ABC$ such that $AB = AC$, point $D$ is on $\overline{AC}$ where $\overline{BD} \perp \overline{AC}$. Let $AC$, $CD$ be integers with $BD^{2} = 77$. Determine the minimal value of $AC$ possible.
A) 10
B) 11
C) 12
D) 13
E) 14

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