
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 $f(x) = 3\sin \omega x + 4\cos \omega x$ where $\omega > 0$ has no zeros but has extreme points in the interval $(0, \pi)$, determine the range of $3\cos (\pi \omega) + 4\sin (\pi \omega)$.

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