
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 list of the first 12 positive integers such that for each \(2 \le i \le 12\), either \(b_i+1\) or \(b_i-1\) or both appear somewhere before \(b_i\) in the list, find the number of such lists.

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