
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
Given that $f$: $x→|x|+1$ is a mapping from non-empty set $A$ to non-empty set $B$, if $A={-1,0,1}$ and set $B$ has only two elements, then $B=$ _______; if $B={1,2}$, then the number of sets $A$ that satisfy the condition is _______.

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