
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
Given the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n} - \frac{1}{2}$, where $\overrightarrow{m}=( \sqrt{3}\sin x,\cos x)$ and $\overrightarrow{n}=(\cos x,-\cos x)$.
1. Find the range of the function $y=f(x)$ when $x\in[0, \frac{\pi}{2}]$.
2. In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it is given that $c=2$, $a=3$, and $f(B)=0$. Find the value of side $b$.

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