
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 the sequence $\{a_n\}$ is an arithmetic progression with a non-zero common difference $d$, and $S_n$ represents the sum of its first $n$ terms. If $a_3$, $a_4$, and $a_8$ form a geometric progression, then among the following four conclusions:  
① $a_1d < 0$;  
② $dS_4 < 0$;  
③ $S_8 = -20S_4$;  
④ The common ratio of the geometric progression $a_3$, $a_4$, $a_8$ is 4.  
Which of them are correct?

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