
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 any positive integer  $n$ , the sum  $1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{n}$  is written in the lowest form  $\frac{p_n}{q_n}$ ; that is,  $p_n$  and  $q_n$  are relatively prime positive integers. Find all  $n$  such that  $p_n$  is divisible by  $3$ .

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