
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
Find natural numbers \(a, b, c\) such that for any \(n \in \mathbf{N}\) with \(n > 2\), the following inequality holds:
\[ b - \frac{c}{(n-2)!} < \frac{2^{3}-a}{2!} + \frac{3^{3}-a}{3!} + \cdots + \frac{n^{3}-a}{n!} < b. \]

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