
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 sequence {a_n} of positive terms, and $\sqrt{a_1} + \sqrt{a_2} + \ldots + \sqrt{a_n} = n^2 + n$, find the value of $a_1 + \frac{a_2}{2} + \ldots + \frac{a_n}{n}$.

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