
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 a list of the first 12 positive integers ($a_1$, $a_2$, ... $a_{12}$) such that for each $2\le i\le12$, both $a_i + 1$ and $a_i-1$ appear somewhere before $a_i$ in the list, calculate the number of such lists.

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