
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 triangle \(ABC\), point \(D\) is taken on side \(BC\). It is given that \(AB > AC = 4\), \(AD = 3\), and triangles \(ABD\) and \(ACD\) are isosceles. Find \(BC\). If there are multiple possible answers, list them in any order separated by a semicolon.

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