
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:
1. $AB = AC$,
2. $D$ is a point on $\overline{AC}$ where $\overline{BD} \perp \overline{AC}$,
3. $AC$ and $CD$ are integers, and $BD^2 = 85$.
   
Find the smallest possible value of $AC$.
A) 10  
B) 11  
C) 12  
D) 13  
E) 14

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