
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 an arithmetic sequence $\{ a_{n} \}$ with common difference $d > 0$ and $a_{1} = 1$, let $S_{n}$ denote the sum of the first $n$ terms and $S_{2} \cdot S_{3} = 36$.
(1) Find the value of $d$ and the expression for $S_{n}$.
(2) Find the values of $m, k (m, k \in \mathbb{N}^{\ast})$ such that $a_{m} + a_{m + 1} + a_{m + 2} + \dots + a_{m + k} = 65$.

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