
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 a triangle \(ABC\) where \(AB = AC\), \(D\) is a point on \(\overline{BC}\) such that \(\overline{AD} \perp \overline{BC}\), \(BC\) and \(CD\) are integers, and \(AD^2 = 72\). Find the smallest possible value of \(BC\).
A) 9 
B) 10 
C) 11 
D) 12 
E) 13

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