
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
Let \(a_1, a_2, \cdots, a_9\) be positive integers (which may be the same) such that for any \(1 \leq i<j<k \leq 9\), there exists a \( l(1 \leq l \leq 9) \) different from \(i, j,\) and \(k\) such that \(a_i + a_j + a_k + a_l = 100\). Find the number of ordered 9-tuples \(\left(a_1, a_2, \cdots, a_9\right)\) that satisfy the above condition.
(2017 Western China Mathematical Invitational)

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