
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 the function \( f(x) \) that satisfies the following five conditions:
1. The domain of \( f(x+1) \) is \([-5, 3]\);
2. \( f(x) + f(-x) = 0 \);
3. \( f(-1) = 0 \);
4. \( f(x) \) is monotonically decreasing on \([-4, 0)\);
5. \( f(x) \) has no maximum value.

Determine the solution set of the inequality \( x^3 f(x) \leqslant 0 \).

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