
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 internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively. Given that $a+c=1+ \sqrt {3}$, $b=1$, and $\sin C= \sqrt {3}\sin A$,

$(1)$ Find angle $B$;

$(2)$ Let $f(x)=2\sin (2x+B)+4\cos ^{2}x$. 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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