
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 an odd function $f(x)$ on $\mathbb{R}$ that is a decreasing function. Given $a+b\leq 0$, consider the following inequalities:  
① $f(a) \cdot f(-a) \leq 0$;  
② $f(a) + f(b) \leq f(-a) + f(-b)$;  
③ $f(b) \cdot f(-b) \geq 0$;  
④ $f(a) + f(b) \geq f(-a) + f(-b)$.  
Among these, select the correct inequalities (Write down the numbers of all correct inequalities).

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