
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
Is there any constants $a$, $b$, $c$, such that the equation $1\left(n^{2}-1^{2}\right)+2\left(n^{2}-2^{2}\right)+\cdots+n\left(n^{2}-n^{2}\right)=a{n}^{4}+b{n}^{2}+c$ holds for all positive integers $n$? If so, find the values of $a$, $b$, and $c$; if not, explain why.

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