
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 any two distinct values ${x_1}, {x_2}$ in the domain of the function $f(x)$, the following conclusions are drawn:
$①f({x_1}+{x_2})=f({x_1})⋅f({x_2})$;
$②f({x_1}⋅{x_2})=f({x_1})⋅f({x_2})$;
$③\frac{f({x_1})-f({x_2})}{{x_1}-{x_2}} > 0$;
$④f(\frac{{x_1}+{x_2}}{2}) < \frac{f({x_1})+f({x_2})}{2}$.

When $f(x)=x^2, x\in (0,+\infty)$, the correct conclusion(s) is/are ________.

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