
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 ($b_1$, $b_2$, ... $b_{12}$) be a list of the first 12 positive integers such that for each $2\le$ $i$ $\le12$ either $b_i + 1$ or $b_i-1$ or both appear somewhere before $b_i$ in the list. Additionally, the list must start with 1 and end with 12. How many such lists are there?

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