
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 polar coordinate equation of circle C is ρ² + 2$\sqrt {2}$ρsin(θ + $\frac {π}{4}$) + 1 = 0, and the origin O of the rectangular coordinate system xOy coincides with the pole, and the positive semi-axis of the x-axis coincides with the polar axis. (1) Find the standard equation and a parametric equation of circle C; (2) Let P(x, y) be any point on circle C, find the maximum value of xy.

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