
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
Consider a sequence \((a_1, a_2, \ldots, a_{12})\) of the first 12 positive integers such that for each \(2 \leq i \leq 12\), \(a_i + 1\) or \(a_i - 1\) or both appear somewhere before \(a_i\) in the list. Moreover, each \(a_i\) must be different from \(a_i - 2\) and \(a_i + 2\) when applicable. How many such sequences exist?
- **A)** 48
- **B)** 256
- **C)** 512
- **D)** 1024
- **E)** 2048

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