
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
Let $\triangle ABC$ have sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$, respectively. If $a+c=1+ \sqrt {3}$ and $b=1$, with $\sin C= \sqrt {3}\sin A$,  
(1) Find angle $B$;  
(2) Let $f(x)=2\sin(2x+B)+4\cos^2x$. Find the range of the function $y=f(x)$ in the interval $\left[0, \frac{\pi}{2}\right]$.

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