
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
Crestview's school colors are purple, gold, and blue. The students are designing a flag using three solid-colored horizontal stripes and an optional vertical stripe, which can be either one color or none. How many different flags are possible if adjacent horizontal stripes and the optional vertical stripe may use any of these colors?

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