
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 $f(x)=Asin(ωx+φ)(A>0,ω>0,0<φ<\frac{π}{2})$ with a maximum value of $2$ and a minimum positive period of $π$, where $f(-\frac{π}{6})=0$. Find:<br/>
$(1)$ The analytical expression of $f(x)$;<br/>
$(2)$ The intervals where $f(x)$ is monotonically increasing.

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