
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
Let set $A=\left\{x \mid x^{2}-[x]=2\right\}$ and set $B=\{x \mid x<2\}$, where the symbol $[x]$ denotes the greatest integer less than or equal to $x$. Find $A \cap B$.

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