
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 positive integers \( a_{1}, a_{2}, \cdots, a_{9} \) (which can be the same) such that for any \( 1 \leqslant i < j < k \leqslant 9 \), there exists \( l \) (different from \( i, j, k \) and \( 1 \leqslant l \leqslant 9 \)) such that \( a_{i}+a_{j}+a_{k}+a_{l}=100 \). Determine the number of such ordered nine-tuples \( \left(a_{1}, a_{2}, \cdots, a_{9}\right) \).

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