
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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Let \( P \) be a regular 2006-gon. A diagonal of \( P \) is called good if its endpoints divide the boundary of \( P \) into two parts, each containing an odd number of sides of \( P \). Sides of \( P \) are also called good.

Suppose we divide \( P \) into triangles using 2003 diagonals such that no two diagonals intersect in the interior of \( P \). Determine the maximum number of isosceles triangles with two good sides that can occur in such a triangulation.

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