
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
Determine the correct judgment(s) among the following options (write down the correct option number(s)).
$①$ Set $A={(x,y)|x+y=5}$, $B={(x,y)|x-y=-1}$, then $A∩B={(2,3)}$;
$②$ Let $f(x)$ be a function defined on $R$ such that for any $m$, $n$, $f(m+n)=f(m)⋅f(n)$, and $0 < f(x) < 1$ when $x > 0$, then $f(0)=1$, and $f(x) > 1$ when $x < 0$;
$③$ The domain of the function $f(x)= \frac {33x-1}{ax^{2}+ax-3}$ is $R$, then the range of the real number $a$ is $-12 < a < 0$;
$④$ The function $y=-\log _{2}x$ satisfies $f(\frac {x_{1}+x_{2}}{2})\leqslant \frac {f(x_{1})+f(x_{2})}{2}$ for any $x_{1}$, $x_{2}$ in its domain.

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