
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 $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$, and $S_6 > S_7 > S_5$, the following five statements are given:  
① $d < 0$; ② $S_n > 0$; ③ $S_{12} < 0$; ④ The maximum term in the sequence $\{S_n\}$ is $S_{11}$; ⑤ $|a_6| > |a_7|$.  
Among these, the correct statement numbers are: \_\_\_\_\_\_.

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