
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 the function $y=f(x)$, if there exists $x_0$ in its domain such that $x_0 \cdot f(x_0) = 1$, then $x_0$ is called the "inverse proportion point" of the function $f(x)$. Among the following functions, those that have an "inverse proportion point" are __________.  
① $f(x) = -2x + 2\sqrt{2}$;  ② $f(x) = \sin x$, $x \in [0, 2\pi]$;  
③ $f(x) = x + \frac{1}{x}$, $x \in (0, +\infty)$; ④ $f(x) = e^x$;  ⑤ $f(x) = -2\ln x$.

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