
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
For a function $f(x)$ defined on $\mathbb{R}$, whose graph is continuous without breaks, and there exists a constant $l$ ($l \in \mathbb{R}$) such that $f(x+l) + lf(x) = 0$ for all real numbers $x$, then $f(x)$ is called an "$l$-companion function". The following conclusions about "$l$-companion functions" are given:  
 ① $f(x)=0$ is the only constant function that is an "$l$-companion function";  
 ② $f(x) = x$ is not an "$l$-companion function";  
 ③ $f(x)=x^2$ is an "$l$-companion function";  
 ④ An "$l$-companion function" has at least one zero.  
Identify the **incorrect** numbers. (Fill in all incorrect conclusion numbers).

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