
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
Four events: ① When $x \in \mathbb{R}$, the equation $x^2+1=0$ has no real solutions; ② If $x \in \mathbb{R}$ and $x \neq 0$, then $x > \frac{1}{x}$; ③ The function $y= \frac{1}{x}$ is increasing over its domain; ④ If $a^2+b^2=0$ and $a, b \in \mathbb{R}$, then $a=b=0$. The random event is \_\_\_\_\_\_.

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