
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
If the sequence $\{a_n\}$ is a positive term sequence, and $\sqrt{a_1}+ \sqrt{a_2}+ \sqrt{a_3}+...+ \sqrt{a_n}=n^2+n$, then $\frac{a_1}{1}+ \frac{a_2}{2}+...+ \frac{a_n}{n} =$ ______.

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