
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  $2006$ -gon. A diagonal is called *good* if its endpoints divide the boundary of  $P$  into two parts, each composed of an odd number of sides of  $P$ . The sides of  $P$  are also called *good*.
Suppose  $P$  has been dissected into triangles by  $2003$  diagonals, no two of which have a common point in the interior of  $P$ . Find the maximum number of isosceles triangles having two good sides that could appear in such a configuration.

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