
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]


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The function $f(x)=\sin(\omega x+\varphi)$ $(\omega > 0, |\varphi| < \frac{\pi}{2})$ has a monotonic decreasing interval of $\left[ \frac{5\pi}{12}, \frac{11\pi}{12}\right]$ within one of its periods. The graph of $y=f(x)$ is first translated to the left by $\frac{\pi}{4}$ units, and then all the points on the graph have their x-coordinates halved (the y-coordinates remain unchanged). The function corresponding to the resulting graph is denoted as $g(x)$.

    (1) Find the analytical expression of $g(x)$;

    (2) Find the maximum and minimum values of $g(x)$ in the interval $\left[0, \frac{\pi}{4}\right]$.

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