
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 that the maximum value of the function $$f(x)=4\cos{x}\sin{(x+\frac{\pi}{6})}+a$$ is 2, find:
(I) The value of $a$ and the minimum positive period of $f(x)$;
(II) The range of $y=f(x)$ on $\left[- \frac{5}{12}\pi, 0\right]$.

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