
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 that each list of length 5 must include the integers 1,2,3,4,5, determine the number of valid lists where for every integer $i$ ($2 \le i \le 5$), it must either have $i+1$ or $i-1$ (or both) before $i$ in the list.

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