
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 proposition(s) among the following four options. (Fill in the serial number(s) of all correct propositions)
$①∀x∈R$, $x^{2}-x+ \frac {1}{4}≥0$;
$②$ All squares are rectangles;
$③∃x∈R$, $x^{2}+2x+2≤0$;
$④$ There exists at least one real number $x$, such that $x^{3}+1=0$.

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