
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 $\triangle ABC$ with the sides opposite to angles $A$, $B$, $C$ being $a$, $b$, $c$ respectively, and it satisfies $a=1$, $\frac {\sin (2A+B)}{\sin A}=2(1-\cos C)$.  
$(1)$ Find the value of $b$;  
$(2)$ If the area of $\triangle ABC$ is $\frac {\sqrt {3}}{2}$, find the value of $c$.

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