
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
Given the sequence \(1,2,3,4,5,6\), find the number of ways to rearrange the terms so that no three consecutive terms are increasing, no three consecutive terms are decreasing, and no term appears at its original position.

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