
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, C are a, b, c, respectively, and $c - a \cos B = \frac{\sqrt{2}}{2} b$.
(I) Find angle A;
(II) If $c = 4\sqrt{2}$ and $\cos B = \frac{7\sqrt{2}}{10}$, find the area of triangle ABC.

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