
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 $f(x)=a\sin (2\omega x+ \frac {\pi}{6})+ \frac {a}{6}+b$ $(x\in\mathbb{R},a > 0,\omega > 0)$ has a minimum positive period of $\pi$, and the maximum value of $f(x)$ is $\frac {7}{4}$, while the minimum value is $\frac {3}{4}$.  
$(1)$ Find the values of $\omega$, $a$, and $b$;  
$(2)$ Determine the intervals of monotonic increase for $f(x)$.

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