
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
In an arithmetic sequence $\{a_n\}$, let $S_n$ represent the sum of the first $n$ terms, and it is given that $S_6 < S_7$ and $S_7 > S_8$. Based on this information, which of the following statements are correct?
① The common difference $d < 0$.
② $S_9 < S_6$.
③ $a_7$ is the largest term in the sequence.
④ $S_7$ is definitively the maximum value among all sums $S_n$.
(Write down the serial numbers of the correct statements.)

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