
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
The function $f(x)=\sin \omega x$ is increasing in the interval $\left(0, \frac{\pi}{6}\right)$. Then, the correct conclusion(s) is(are) __________ (Fill in all the serial numbers that apply in the blank).

① The function $f(x)=\sin \omega x$ is increasing in the interval $\left(-\frac{\pi}{6},0\right)$;  
② The maximum value of the positive integer $\omega$ that satisfies the condition is $3$;  
③ $f\left(\frac{\pi}{4}\right) \geqslant f\left(\frac{\pi}{12}\right)$.

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