
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]


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Triangle \( \triangle ABC \) is a non-equilateral acute triangle, and point \( O \) is inside \( \triangle ABC \) such that \( OA = OB = OC \). Symmetric points of \( O \) with respect to sides \( BC, CA, \) and \( AB \) are denoted as \( A', B', \) and \( C' \) respectively. Determine the number of quadrilaterals formed using any four points from \( A, B, C, O, A', B', C' \) that are parallelograms.

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