
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
From the permutation \(a_{1} a_{2} \cdots a_{n}\) (\(n \geqslant 10\)), choose 3 elements \(a_{i}, a_{j},\) and \(a_{k}\) (\(1 \leqslant i < j < k \leqslant n\)) such that there are at least 3 elements between \(a_{i}\) and \(a_{j}\), and at least 4 elements between \(a_{j}\) and \(a_{k}\). How many different ways are there to choose them?

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