
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 $f(x)=\sin (2\omega x+ \frac {\pi}{4})$ $(x\in\mathbb{R},\omega > 0)$ has the smallest positive period of $\pi$.  
$(1)$ Find the range of $f(x)$ on $\left[0, \frac {\pi}{2}\right]$ and the value of $x$ when it takes the minimum value;  
$(2)$ Find the intervals of monotonic increase for $f(x)$.

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