
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 $g(x)=2 \sqrt {3}\sin x\cdot \cos x+2\cos ^{2}x+m$ in the interval $\[0, \dfrac {π}{2}\]$. The maximum value of the function in this interval is $6$.

(1) Find the value of the constant $m$;
(2) Find the minimum value of the function $g(x)$ when $x\in R$ and find the corresponding set of $x$ values;
(3) Find the increasing interval of the function $y=g(-x)$.

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