
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
Consider triangle $ABC$ with side lengths opposite angles $A$, $B$, $C$ being $a$, $b$, $c$, respectively. Let $S$ represent the area of triangle $ABC$, which satisfies $S = \frac{\sqrt{3}}{4}(a^2 + c^2 - b^2)$.
(Ⅰ) Find angle $B$;  
(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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