
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, with $c=2\sqrt{3}$, and it is given that $a\sin A - c\sin C = (a-b)\sin B$.

(Ⅰ) Find the value of angle $C$;

(Ⅱ) If $c + b\cos A = a(4\cos A + \cos B)$, find the area of $\triangle ABC$.

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