
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 $f\left(x\right)=|\sin x|\cdot \cos x$, $x\in R$, the following four statements are made:<br/>① One positive period of $f\left(x\right)$ is $2\pi$;<br/>② $f\left(x\right)$ is monotonically increasing on $[-\frac{π}{4}$, $\frac{π}{4}]$;<br/>③ The range of $f\left(x\right)$ is $[-\frac{1}{2}$, $\frac{1}{2}]$;<br/>④ The graph of $f\left(x\right)$ is symmetric about $x=\pi$.<br/>Among them, the correct statements are ____.

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