
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 a Cartesian coordinate system xOy and a polar coordinate system Oθ with the same origin and positive x-axis coinciding with the polar axis, and equal unit lengths, the curve C in the Cartesian coordinate system is defined by the parametric equations: 
$$
\begin{cases}
x = 2\cosφ \\
y = \sinφ
\end{cases}
$$
where φ is the parameter.
(1) In the polar coordinate system, if the curve intersects with the rays θ = $\frac{\pi}{4}$ and θ = -$\frac{\pi}{4}$ at points A and B respectively, find the area of triangle ΔAOB.
(2) In the Cartesian coordinate system, given the parametric equations of line l are:
$$
\begin{cases}
x = 2 + \frac{\sqrt{2}}{2}t \\
y = \frac{\sqrt{2}}{2}t
\end{cases}
$$
where t is the parameter, find the coordinates of the intersection points of curve C and line l.

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