
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
Let \( n \) be a positive integer and \( k_{1}, k_{2}, k_{3}, \ldots, k_{n} \) denote an arbitrary permutation of the integers from 1 to \( n \). What is the maximum value of the expression

\[
\left(1-k_{1}\right)^{2}+\left(2-k_{2}\right)^{2}+\left(3-k_{3}\right)^{2}+\ldots+\left(n-k_{n}\right)^{2}
\]

for an \( n \)-term sequence?

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