
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
Color each vertex of a convex $n$-gon ($n \geqslant 4$) either black or white. If the endpoints of a diagonal have different colors, it is called a "two-colored diagonal". A coloring method is called "good" if the convex $n$-gon can be divided into several triangles using two-colored diagonals. Find the number of good coloring methods.

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