
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 $1,2,3,4,5,6$ can be rearranged so that no three consecutive terms are increasing and no three consecutive terms are decreasing, find the number of ways of rearrangement.

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