
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 \( a > b > c \), \( n \in \mathbf{N} \), and \( \frac{1}{a-b} + \frac{1}{b-c} \geqslant \frac{n}{a-c} \) always holds, find the maximum value of \( n \).

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