
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 $0 < a < b < c$ and $f(a)=f(b)=f(c)=0$. Determine the correct conclusion(s) from the following options:
$①f(0)f(1) > 0$;
$②f(0)f(1) < 0$;
$③f(0)f(3) > 0$;
$④f(0)f(3) < 0$.
(Fill in the sequence number(s) for the correct conclusion(s))

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