
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 a sequence $\{a_n\}$ that satisfies $(a_1 + a_2 + \cdots + a_n = n^2)$, if for a given $k \in \mathbb{N}^*, \frac{1}{a_k}, \frac{1}{a_p}, \frac{1}{a_r}$ form an arithmetic sequence, where $(k < p < r)$, determine the relationship between $k, p,$ and $r$.

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