
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 $(b_1, b_2, ..., b_{12})$ is a list of the first 12 positive integers, where for each $2 \leq i \leq 12$, either $b_i + 1$, $b_i - 1$, or both appear somewhere in the list before $b_i$, and all even integers precede any of their immediate consecutive odd integers, find the number of such lists.

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