
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 $ABC$, let the sides opposite angles $A$, $B$, $C$ be $a$, $b$, $c$ respectively, and $\frac{b-c}{a} = \frac{\sin A-\sin C}{\sin B+\sin C}$.

$(I)$ Find the angle $B$;

$(II)$ If $a+c=5$ and the area of $\triangle ABC$ is $\dfrac{3\sqrt{3}}{2}$, find the length of side $b$.

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