
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
Consider the inequalities \( n_{1}+\ldots+n_{N} \leqslant n \) with non-negative or positive integers \( n_{i}, i=1, \ldots, N \). Count the number of ordered vectors \(\left(n_{1}, \ldots, n_{N}\right)\) satisfying the inequalities \( n_{1}+\ldots+n_{N} \leqslant n, n \geqslant 1, N \geqslant 1 \).

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