
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 an ellipse $C$ with its center $O$ at the origin, its major axis along the x-axis, its focal distance is 6, and its minor axis is 8.
(1) Find the equation of ellipse $C$;
(2) A line passing through point $(-5, 0)$ with a slope of $\frac{\pi}{4}$ intersects ellipse $C$ at points $A$ and $B$. Find the area of $\triangle ABO$.

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