
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 $f(x)=\cos x\sin 2x$, determine the correct conclusion(s) among the following:

1. The graph of $y=f(x)$ is symmetrical about the center $(\pi, 0)$;
2. The graph of $y=f(x)$ is symmetrical about the line $x=\frac{\pi}{2}$;
3. The maximum value of $y=f(x)$ is $\frac{\sqrt{3}}{2}$;
4. The function $y=f(x)$ is both an odd function and a periodic function.

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