
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 $f(x) = |\cos x| \cdot \sin x$, consider the following five statements:  
① $f\left( \frac {2015\pi}{3}\right)=- \frac { \sqrt {3}}{4}$;  
② If $|f(x_1)| = |f(x_2)|$, then $x_1 = x_2 + k\pi$ ($k \in \mathbb{Z}$);  
③ $f(x)$ is monotonically increasing in the interval $\left[- \frac {\pi}{4}, \frac {\pi}{4}\right]$;  
④ The smallest positive period of the function $f(x)$ is $\pi$;  
⑤ The graph of $f(x)$ is centrally symmetric about the point $(\pi, 0)$.  
Among these statements, the correct ones are \_\_\_\_\_\_.

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