
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 the function $f(x) = \sin\frac{1}{x}$, the following statements are made:<br/>① The range of $f(x)$ is $\left[-1,1\right]$;<br/>② $f(x)$ is a periodic function;<br/>③ $f(x)$ is monotonically decreasing on $[\frac{2}{\pi}, +\infty)$;<br/>④ For any $m \in \left[-1,1\right]$, the equation $f(x) = m$ has infinitely many solutions in the interval $(0,1)$.<br/>The correct statements are ____.

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