
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 curve C, any point M on the curve is such that the distance from M to the point F(0, 1) is 1 unit less than its distance to the line l: y = -2.
(1) Find the equation of the curve C.
(2) The line passing through the point P(2, 2) intersects the curve C at points A and B. Let $\overrightarrow {AP} = \lambda \overrightarrow {PB}$. When the area of triangle ΔAOB is $4 \sqrt {2}$ (where O is the origin of the coordinates), find the value of λ.

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