
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 a polar coordinate system where the pole O coincides with the origin and the polar axis coincides with the positive half of the x-axis, the polar coordinates of points A and B are respectively given as $(2, \pi)$ and $\left(2 \sqrt{2}, \frac{\pi}{4}\right)$. The curve C is described by the parametric equations: 
$$
\begin{cases}
x=\sin{\alpha} \\
y=1+\cos^2{\alpha}
\end{cases} (\alpha \text{ is the parameter}).
$$
(I) Calculate the area of triangle $\triangle AOB$.  
(II) Find the intersection points of line AB and curve C.

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