
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 $g(x)=2 \sqrt {3}\sin x\cdot\cos x+2\cos ^{2}x+m$ has a maximum value of $6$ in the interval $\left[0, \frac {\pi}{2}\right]$  
$(1)$ Find the value of the constant $m$;  
$(2)$ Find the increasing interval of the function $y=g(-x)$.

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