
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
Let $f(x) = \sin(x\cos x)$. The following conclusions are given:<br/>① $f(x)$ is an odd function;<br/>② When $x∈(0,\frac{π}{2})$, $f(x) \gt 0$;<br/>③ $f(x)$ is a periodic function;<br/>④ $f(x)$ has infinitely many zeros.<br/>The correct numbers of the conclusions are ____. (Write down the numbers of all correct conclusions)

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