
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
Suppose $f\colon x \mapsto |x|+1$ is a mapping from a non-empty set $A$ to a non-empty set $B$. If $A = \{-1, 0, 1\}$ and set $B$ contains only two elements, then $B = \; $? Additionally, if $B = \{1, 2\}$, then the number of possible sets $A$ satisfying the condition is $\; ?$.

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