
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
For positive integers \( n \), let \( c_{n} \) be the smallest positive integer for which \( n^{c_{n}}-1 \) is divisible by 210, if such a positive integer exists, and \( c_{n} = 0 \) otherwise. What is \( c_{1} + c_{2} + \cdots + c_{210} \)?

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