
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 the rectangular coordinate system, a polar coordinate system is established with the origin as the pole and the positive semi-axis of the x-axis as the polar axis. Given circle C: ρ = 2cosθ - 2sinθ, and the parametric equation of line l is x = t, y = -1 + 2√2t (t is the parameter). Line l intersects with circle C at points M and N, and point P is any point on circle C that is different from M and N.

1. Write the rectangular coordinate equation of C and the general equation of l.
2. Find the maximum area of triangle PMN.

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