
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
Let \( (1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}) = \frac{p_n}{q_n} \), where \( p_n \) and \( q_n \) are relatively prime positive integers. For which \( n \) is \( q_n \) not divisible by 5?

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