
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 polar coordinate system, the coordinates of point M are $$(3, \frac{\pi}{2})$$, and the equation of curve C is $$\rho = 2\sqrt{2}\sin\left(\theta + \frac{\pi}{4}\right)$$; taking the pole as the origin of the coordinate system and the positive half-axis of the x-axis as the polar axis, a line l with a slope of -1 passes through point M.  
(1) Find the Cartesian equations of line l and curve C;  
(2) If P is any point on curve C, and line l intersects curve C at points A and B, find the maximum area of $\triangle PAB$.

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