
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 that \( (a_1, a_2, \ldots, a_{15}) \) is a list of the first 15 positive integers such that for each \( 2 \leq i \leq 15 \), either \( a_i + 1 \) or \( a_i-1 \) (or both) appear somewhere before \( a_i \) in the list, and \( a_1 \) must be either 1 or 2, and \( a_{15} \) must be either 14 or 15, determine the number of such lists.

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