
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
In the convex pentagon $ABCDE$, each side and diagonal must be colored either red or blue such that in the perimeter of any triangle formed by three vertices, both colors are present. How many ways can this be done?

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