
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 of lengths $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively. Let $S$ be the area of $\triangle ABC$, satisfying $S= \frac{ \sqrt{3}}{4}(a^{2}+c^{2}-b^{2})$.  
(I) Find $B$;  
(II) If $b=\sqrt{3}$, find the maximum value of $(\sqrt{3}-1)a+2c$.

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