
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 $f(x)=2\sin \frac{\pi}{6}x\cos \frac{\pi}{6}x$, let $g(t)$ denote the slope of the line passing through two points $A(t,f(t))$ and $B(t+1,f(t+1))$.

(I) Find the value of $g(0)$;

(II) Derive an expression for the function $g(t)$ and determine its range of values on the interval $\left[-\frac{3}{2}, \frac{3}{2}\right]$.

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