
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
Let \(X\) be a given number. Determine the number of ways to order \(X\) crimson flowers, \(X\) scarlet flowers, and \(X\) vermillion flowers in a row such that no two flowers of the same hue are adjacent. (Flowers of the same hue are mutually indistinguishable.) Find the value of \(Y\).

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