
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
If two numbers \(a\) and \(b\) give the same remainders when divided by \(c\), then \(a\) and \(b\) are called congruent modulo \(c\). Find the values of \(x\) for which the numbers \(x^{5}\) and \(x\) are congruent modulo 210.

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