
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 that the vertex of a parabola is at the origin and the center of the circle $(x-2)^2 + y^2 = 4$ is exactly the focus of the parabola.

1. Find the equation of the parabola.
2. A line with a slope of 2 passes through the focus of the parabola and intersects the parabola at points A and B. Find the area of triangle OAB.

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