
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
Sets $A$ and $B$ are both subsets of the real number set $\mathbb{R}$. Given a mapping: $f: A \rightarrow B$, which maps the element $x$ in set $A$ to the element $x^3 - x + 1$ in set $B$. Then, under the mapping $f$, the set composed of elements in set $A$ that correspond to the element $1$ in set $B$ is

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