
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
For high school students, consider the curve $xy - x^2 = 1$. Which of the following statements are true? (1) It represents a circle; (2) It is symmetric about both coordinate axes; (3) It is symmetric about the origin; (4) $|x| \geq 2$, $|y| \geq 2$. Fill in the corresponding number(s).

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