
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 triangle $ABC$, with the internal angles at $A$, $B$, and $C$ corresponding to the sides $a$, $b$, $c$ respectively. Given that $(1-\tan A)(1-\tan B)=2$:  
(1) Find the angle $C$.  
(2) If $b=2\sqrt{2}$ and $c=4$, find the area $S_{\triangle ABC}$ of the triangle $ABC$.

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