
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
A function $f(x) = \sin(\omega x + \varphi)$ where $\omega > 0$ and $|\varphi| < \frac{\pi}{2}$ has a monotonically decreasing interval of $[\frac{5\pi}{12}, \frac{11\pi}{12}]$ in one of its periods.

(1) Find the analytical expression for $f(x)$;
(2) After shifting the graph of $y=f(x)$ to the right by $\frac{\pi}{6}$ units and then halving the horizontal coordinates of all points (without changing vertical coordinates), the resulting graph corresponds to function $g(x)$. Find the maximum and minimum values of $g(x)$ on $[\frac{\pi}{8}, \frac{3\pi}{8}]$.

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