
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
The function $f(x)=\sin(\omega x+\phi)$ ($\omega > 0$, $|\phi| < \frac{\pi}{2}$) is decreasing monotonically in its period interval $\left[\frac{5\pi}{12}, \frac{11\pi}{12}\right]$. Transform the graph of $y=f(x)$ by first shifting it to the left by $\frac{\pi}{4}$ units, and then scaling the x-coordinates of all points on the graph to half of their original value (leaving the y-coordinates unchanged). Let the resulting function be $g(x)$.
(Ⅰ) Find the analytical expression for $g(x)$;
(Ⅱ) Find the maximum and minimum values of $g(x)$ in the interval $x \in \left[0, \frac{\pi}{4}\right]$.

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