
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $A$ is an acute angle, and $b\sin A\cos C + c\sin A\cos B = \frac{\sqrt{3}}{2}a$.  
(1) Find the magnitude of angle $A$;  
(2) Let the function $f(x) = \tan A\sin \omega x\cos \omega x - \frac{1}{2}\cos 2\omega x$ ($\omega > 0$), and the distance between two adjacent axes of symmetry on its graph is $\frac{\pi}{2}$. If the graph of $y = f(x)$ is translated to the left by $\frac{\pi}{4}$ units to obtain the graph of $y = g(x)$, find the range of $g(x)$ in the interval $\left[-\frac{\pi}{24}, \frac{\pi}{4}\right]$.

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