
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 $f(x)=2\sqrt{3}\sin \omega x\cdot \cos \omega x+2\cos^2 \omega x -1$ ($\omega > 0$) has the smallest positive period of $\frac{\pi}{2}$, determine the range of the function $y=f(x)$ when $x\in [0,\frac{\pi}{4}]$.

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