
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 that $1^{2}= \frac{1}{6}\times1\times2\times3$, $1^{2}+2^{2}= \frac{1}{6}\times2\times3\times5$, $1^{2}+2^{2}+3^{2}= \frac{1}{6}\times3\times4\times7$, $1^{2}+2^{2}+3^{2}+4^{2}= \frac{1}{6}\times4\times5\times9$, then $1^{2}+2^{2}+\cdots+n^{2}= \quad$.

(Where $n\in\mathbb{N}^{+}$)

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