
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 $f(x)=2\sin ^{2}x+ \sqrt {3}\sin 2x+1.$, find:
$(1)$ The interval(s) where $f(x)$ is monotonically increasing;
$(2)$ The maximum and minimum values of $f(x)$ on $\[0, \dfrac {π}{2}\]$.

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