
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
The function \( f(x) \) (where \( x \in \mathbf{R} \)) satisfies: \( f(-4) = f(1) = 0 \). In the intervals \([0, 3]\) and \([3, +\infty)\), the function is decreasing and increasing respectively. Determine the solution set for the inequality \( x^3 f(x) < 0 \).

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