
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 vectors $\overrightarrow{m}=(2\cos \omega x, \sqrt{3})$, $\overrightarrow{n}=(\sin \omega x, 2\cos ^{2}\omega x-1)$, where $\omega > 0$, and $f(x)=\overrightarrow{m}\cdot \overrightarrow{n}$, find:

1. If the function $y=f(x)$ has a minimum positive period of $\pi$, determine the intervals where the function $y=f(x)$ is decreasing.
2. If the function $y=f(x)$ has exactly one extremum in the interval $({0,\frac{π}{2}})$, find the range of values for $\omega$.

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