
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
Given a function $y=f(x)$, if there exists an $x\_0$ in its domain such that $x\_0 \cdot f(x\_0) = 1$ holds, then $x\_0$ is called the "reciprocal point" of the function $f(x)$. Among the following functions, the one(s) with a "reciprocal point" is/are _____.
$①f(x)=-2x+2 \sqrt {2}$; $②f(x)=\sin x$, $x \in [0,2π]$;
$③f(x)=x+ \frac {1}{x}$, $x \in (0,+\infty)$; $④f(x)=e^{x}$; $⑤f(x)=-2\ln x$.

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