
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
Determine the prime numbers \( p \) such that the decimal representation of the fraction \( \frac{1}{p} \) has a repeating sequence of length 5.

Note: If the decimal representation of a number has a periodically repeating sequence of digits, the length of the smallest repeating sequence of digits is the period length of the decimal representation. For example, \( \frac{61}{495} = 0.1232323\ldots \) has repeating sequences 23, 2323, etc., but the length of the smallest repeating sequence is 2, which is the period length.

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