
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 $ABC$, with the sides opposite angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively, it is known that $\frac{a-c}{a-b}=\frac{\sin(A+C)}{\sin A + \sin C}$.  
(I) Determine the size of angle $C$.  
(II) Given that $\left|\overrightarrow{CA}-\frac{1}{2}\overrightarrow{CB}\right| = 2$, find the maximum area of triangle $ABC$.

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