
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
Which of the following correspondences $f$ are functions from set $A$ to set $B$?  
(1) $A=\{1,2,3\}$, $B=\{7,8,9\}$, $f(1)=f(2)=7$, $f(3)=8$  
(2) $A=B=\{1,2,3\}$, $f(x)=2x-1$  
(3) $A=B=\{x|x\geq-1\}$, $f(x)=2x+1$  
(4) $A=\mathbb{Z}$, $B=\{-1,1\}$, for odd $n$, $f(n)=-1$, for even $n$, $f(n)=1$.

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