
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 that $S_n$ is the sum of the first $n$ terms of the arithmetic sequence $\{a_n\} (n \in N^*)$, and $S_5 > S_6 > S_4$. Determine the sequence of correct propositions among 1. The maximum term in the sequence $\{S_n\}$ is $S_{10}$. 2. The common difference $d$ of the sequence $\{a_n\}$ is less than 0. 3. $S_{10} > 0$. 4. $S_{11} < 0$.

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