
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

In the list $1, 2, \ldots, 2016$, two numbers $a < b$ are marked, dividing the sequence into 3 parts (some parts might be empty). After this, the list is shuffled in such a way that $a$ and $b$ remain in their places, and none of the other 2014 numbers stay in the same part where they originally were. In how many ways can $a$ and $b$ be chosen?

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