
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 $A$, $B$, $C$ are respectively $a$, $b$, $c$, and it is given that $a\sin B+ \sqrt{3}a\cos B= \sqrt{3}c.$  
(I) Find the magnitude of angle $A$;  
(II) Given the function $f(x)=\lambda\cos^2(\omega x+ \frac{A}{2})-3$ $(\lambda > 0,\omega > 0)$ has a maximum value of $2$, and the graph of $y=f(x)$ is stretched horizontally to $1.5$ times its original length without changing the vertical coordinates to obtain the graph of $y=g(x)$. If the smallest positive period of $y=g(x)$ is $\pi$, when $x\in[0, \frac{\pi}{2}]$, find the range of $f(x)$.

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