
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 respectively a, b, and c. If $(2a + b)\cos C + c\cos B = 0$.
(1) Find angle C;
(2) If $c = \frac{2\sqrt{6}}{3}$ and $\sin A \cos B = \frac{\sqrt{3} - 1}{4}$, find the area of $\triangle ABC$.

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