
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 $2a_{n+1}=a_n+a_{n+2}+k$ ($n\in\mathbb{N}^*, k\in\mathbb{R}$), and $a_1=2$, $a_3+a_5=-4$.

(1) If $k=0$, find the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$.

(2) If $a_4=-1$, find the general formula for the sequence $\{a_n\}$.

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