
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
Let the domain of the function $f(x)$ be $D$. If for any $x_{1} \in D$, there exists a unique $x_{2} \in D$ such that $\frac{f(x_{1})+f(x_{2})}{2}=c$ (where $c$ is a constant), then the function $f(x)$ is said to have a mean value of $c$ on $D$. Among the following five functions: ①$y=x$; ②$y=|x|$; ③$y=x^{2}$; ④$y=\frac{1}{x}$; ⑤$y=x+\frac{1}{x}$, the numbers of the functions that satisfy the mean value of $2$ on their domains are ____.

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