
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. $f\left(\frac{2014\pi}{3}\right) = -\frac{\sqrt{3}}{4}$;
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 period of the function $f(x)$ is $\pi$;
5. The graph of $f(x)$ is centrally symmetric about the point $\left(-\frac{\pi}{2}, 0\right)$.

Among these statements, the correct ones are \_\_\_\_\_\_.

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