
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 polygon $P$ be a regular 2016-sided polygon.
1. If a diagonal of $P$ divides $P$ into two parts (the sides of $P$ are not considered diagonal), and each part contains an even number of sides of $P$, then this diagonal is called a good diagonal. A convex $m$-gon ($4 < m \leqslant 1008$) with its sides being good diagonals and vertices as vertices of $P$ is called a good convex $m$-gon. Calculate the number of good convex $m$-gons.
2. If a diagonal of $P$ divides $P$ into two parts (the sides of $P$ are not considered diagonal), and each part contains an odd number of sides of $P$, then this diagonal is called a bad diagonal. A convex $m$-gon ($4 < m \leqslant 1008$) with its sides being bad diagonals and vertices as vertices of $P$ is called a bad convex $m$-gon. Calculate the number of bad convex $m$-gons.

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