
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 nine positive integers \( a_{1}, a_{2}, \cdots, a_{9} \) (allowing repetitions) such that for any \( 1 \leqslant i < j < k \leqslant 9 \), there exists an \( l \) (where \( 1 \leqslant l \leqslant 9 \) and \( l \) is different from \( i, j, k \)) satisfying:
\[ a_{i} + a_{j} + a_{k} + a_{l} = 100. \]

Determine the number of ordered 9-tuples \( (a_{1}, a_{2}, \cdots, a_{9}) \) that meet the specified condition.

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