
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 $f(x)=\sin (\omega x+ \frac {\pi}{4})$, where $\omega > 0$, $x\in\mathbb{R}$.  
$(1)f(0)=$ \_\_\_\_\_\_ ；  
$(2)$ If the smallest positive period of the function $f(x)$ is $\pi$, and when $x\in[0, \frac {\pi}{2}]$, find the maximum value of $f(x)$.

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