
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
Given that $a$, $b$, $c$ are the sides opposite the angles $A$, $B$, $C$ of triangle $ABC$ respectively, and it is known that $a\cos{C} + (c-2b)\cos{A} = 0$.

(Ⅰ) Find the value of angle $A$.  
(Ⅱ) If $a = 2$, determine the maximum value of the area of triangle $ABC$.

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