
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 $\{a_n\}$ whose sum of the first n terms is $S_n$, if for $n > 1$, the relationship $2a_n = a_{n+1} + a_{n-1}$ holds, and given that $S_3 < S_5 < S_4$, find the positive integer value of $n$ such that $S_{n-1} \cdot S_n < 0$ (for $n > 1$).

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