
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
Among the following correspondences from set $A$ to set $B$ denoted by $f$, which is a function?

$(1)$ $A=\{-1,0,1\}$, $B=\{0,1\}$, $f$: Squaring the numbers in $A$

$(2)$ $A=\{0,1\}$, $B=\{-1,0,1\}$, $f$: Taking the square root of the numbers in $A$

$(3)$ $A=\mathbb{Z}$, $B=\mathbb{Q}$, $f$: Taking the reciprocal of the numbers in $A$

$(4)$ $A=\mathbb{R}$, $B=$ {positive real numbers}, $f$: Taking the absolute value of the numbers in $A$

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