
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 $$f(x)= \sqrt {3}\sin(\omega x+\omega)-\cos(\omega x+\omega)$$ where $$- \frac {\pi}{2}<\phi<0$$ and $$\omega>0$$, it is known to be an even function, and the distance between two adjacent axes of symmetry of the graph of $$y=f(x)$$ is $$\frac {\pi}{2}.$$  
(1) Find the value of $$f\left( \frac {\pi}{24}\right)$$;  
(2) After translating the graph of $$y=f(x)$$ to the right by $$\frac {\pi}{6}$$ units and then stretching the x-coordinates of the points on the obtained graph by a factor of 4 while keeping the y-coordinates unchanged, we get the graph of the function $$y=g(x)$$. Determine the intervals of monotonicity for $$y=g(x)$$ and find its maximum and minimum values on the interval $$\left[- \frac {\pi}{3}, \frac {5\pi}{6}\right].$$

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