
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 infinite arithmetic sequence $\{a_n\}$ with the sum of the first $n$ terms as $S_n$,
(Ⅰ) If the first term $a_1= \frac {3}{2}$ and the common difference $d=1$, find the positive integer $k$ that satisfies $S_{k^2} = (S_k)^2$;
(Ⅱ) Find all infinite arithmetic sequences $\{a_n\}$ such that $S_{k^2} = (S_k)^2$ holds for all positive integers $k$.

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