
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 $(b_1, b_2, \dots, b_7)$ be a sequence of the first 7 positive integers such that for each $2 \le j \le 7$, either $b_j + 2$ or $b_j - 2$ (or both) must appear somewhere before $b_j$ in the sequence. Find the number of such sequences.

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