
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 $f(x)=2\sin (\omega x+\frac{π}{4})$ where $\omega\ \ \gt 0$, and the range of $f(x)$ on the interval $\left[-1,1\right]$ is $\left[m,n\right]$ with $n-m=3$, find the value of $\omega$.

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