
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 $f(x) = x^3 - 6x^2 + 9x - abc$, where $a < b < c$, and $f(a) = f(b) = f(c) = 0$. The following conclusions are given:  
① $f(0)f(1) > 0$;        ② $f(0)f(1) < 0$;  
③ $f(0)f(3) > 0$;        ④ $f(0)f(3) < 0$.  
Among these conclusions, the correct ones are \_\_\_\_\_\_\_\_．

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