
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
The school has updated its colors to include blue along with purple and gold. Using these three colors, how many different flags can the students design if the flag consists of three solid-colored horizontal stripes and adjacent stripes may be the same color?

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