
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 on 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}
user