
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 positive integer \( n \), Vera performs the following operation: she adds 3 to it repeatedly until she obtains a number divisible by 5 (if the initial number is already divisible by 5, no addition is needed), and then divides the resulting number by 5. She performs the same operation on the resulting quotient, and continues this process indefinitely. For which values of \( n \) can she not obtain 1 through this sequence of operations?

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