
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 △ABC, the sides opposite to angles A, B, and C are denoted as a, b, and c, respectively. Given that $c \cdot \cos B + (b - 2a) \cos C = 0$:  
(1) Determine the size of angle C.  
(2) If $c=2$ and $a+b=ab$, find the area of △ABC.

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