
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 $u_n=n^4+n^2$, define $\Delta^1(u_n)=u_{n+1}-u_n$ and, for all integers $k>1$, $\Delta^k(u_n)=\Delta^1(\Delta^{k-1}(u_n))$. Find the value of $k$ for which the sequence $\Delta^k(u_n)=0$ for all $n$.

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