
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 the sum of the first $n$ terms denoted by $S_n$, it satisfies the condition $a_3 + a_5 = a_4 + 8$.

(Ⅰ) Find the value of $S_7$.

(Ⅱ) If $a_1 = 2$ and the terms $a_3$, $a_{k+1}$, and $S_k$ form a geometric sequence, find the value of the positive integer $k$.

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