
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
An \( n \)-sided polygon (\( n \in \mathbb{N}, n \geq 3 \)) has all its sides labeled as \( a_1, a_2, a_3, \cdots, a_n \) in sequence. Each side is to be colored with one of three colors: red, yellow, or blue such that no two adjacent sides share the same color. What is the total number of ways to color the sides of the polygon?

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