
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 any real numbers $a$, $b$, $c$, the numbers of the true propositions among the following statements are ______.<br/>① $a=b$ is a necessary and sufficient condition for $ac=bc$;<br/>② "$a+5$ is an irrational number" is a necessary and sufficient condition for "$a$ is an irrational number";<br/>③ "$a^{2}=b^{2}$" is a necessary but not sufficient condition for "$a=b$";<br/>④ $\exists x\in R$, $x^{2} \lt 1$.

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