
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 $f(x)= \sqrt {3}\sin 2x-2\cos ^{2}x$.  
$(1)$ Find the value of $f\left( \dfrac {\pi}{6}\right)$;  
$(2)$ Find the intervals where $f(x)$ is monotonically increasing.

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