
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 the arithmetic sequence $\{a_n\}$, $S_n$ is the sum of its first $n$ terms, and it is given that $S_6 < S_7$ and $S_7 > S_8$. Then:

① The common difference $d < 0$  
② $S_9$ is definitely less than $S_6$  
③ $a_7$ is the largest term among all terms  
④ $S_7$ is definitely the maximum value among all $S_n$.  
Among these, the correct ones are ______. (Fill in the correct serial numbers)

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