
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 which of the following correspondences is a mapping from set $A$ to set $B$.
1) Let $A=\{1,2,3,4\}$, $B=\{3,4,5,6,7,8,9\}$, correspondence rule $f$: $x\rightarrow 2x+1$;
2) Let $A=\{0,1,2\}$, $B=\{-1,0,1,2\}$, correspondence rule $f$: $x\rightarrow y=2x-1$;
3) Let $A=\mathbb{N}^*$, $B=\{0,1\}$, correspondence rule $f$: $x\rightarrow$ the remainder when $x$ is divided by $2$;
4) $A=B=\mathbb{R}$, correspondence rule $f$: $x\rightarrow y=\pm \sqrt{x}$.

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