
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 $\sqrt{{a_1}}+\sqrt{{a_2}}+⋯+\sqrt{{a_n}}={n^2}+3n(n\in N^{*})$, then $a_{2}=$______,$\frac{{{a_1}}}{2}+\frac{{{a_2}}}{3}+⋯+\frac{{{a_n}}}{{n+1}}=\_\_\_\_\_\_.$

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