
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
What is the greatest number of equal segments that the set \( a_{1}, a_{2}, \ldots, a_{n} \) can have if \( a_{1} \neq a_{2} \), \( a_{2} \neq a_{3} \), ..., \( a_{n-1} \neq a_{n} \) ?

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