
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
Determine the number of ordered 9-tuples of positive integers \((a_{1}, a_{2}, \cdots, a_{9})\) (elements in the array can be the same) that satisfy the following condition: for any \(1 \leq i < j < k \leq 9\), there exists a different \(l (1 \leq l \leq 9)\) such that
$$
a_{i} + a_{j} + a_{k} + a_{l} = 100.
$$

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