
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 every positive integeer  $n>1$ , let  $k(n)$  the largest positive integer  $k$  such that there exists a positive integer  $m$  such that  $n = m^k$ .

Find   $$ lim_{n \rightarrow \infty} \frac{\sum_{j=2}^{j=n+1}{k(j)}}{n} $$  

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