
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 the sequence ${a_n}$ that satisfies $a_1 + a_2 + ... + a_n = n^2 + 3n (n \in \mathbb{N}^+)$, find the value of $\frac{a_1^2}{2} + \frac{a_2^2}{3} + ... + \frac{a_n^2}{n+1}$ = \_\_\_\_\_\_.

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