
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
Define a function $f(x) = -x - x^3$ on $\mathbb{R}$. Given $x_1 + x_2 \leq 0$, among the following inequalities, the correct ones are:

① $f(x_1)f(-x_1) \leq 0$  
② $f(x_2)f(-x_2) > 0$  
③ $f(x_1) + f(x_2) \leq f(-x_1) + f(-x_2)$  
④ $f(x_1) + f(x_2) \geq f(-x_1) + f(-x_2)$

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