
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
Let \( P \) be a regular 2006-sided polygon. If a diagonal of \( P \), whose endpoints divide the boundary of \( P \) into two parts each containing an odd number of sides, is called a "good diagonal". Note that each side of \( P \) is considered a "good diagonal". Given that 2003 non-intersecting diagonals within \( P \) divide \( P \) into several triangles, determine the maximum number of isosceles triangles with two "good diagonals" produced by this division.

(Problem from the 47th IMO)

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