
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 sequence of positive terms, and $\sqrt{a_1} + \sqrt{a_2} + \ldots + \sqrt{a_n} = n^2 + 3n$, then $\frac{a_1}{2} + \frac{a_2}{3} + \frac{a_3}{4} + \ldots + \frac{a_n}{n+1} =$ ______.

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