
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 in the cartesian coordinate system xOy, point M(x, y) moves on the curve C defined by the parametric equations: $$\begin{cases} x=1+cos\theta \\ y=sin\theta \end{cases}$$ (where θ is the parameter, θ∈R). Establish a polar coordinate system with Ox as the polar axis. The polar coordinate equation of line l is ρcos(θ + $$\frac {π}{4}$$) = 0.
(1) Write the standard equation of curve C and the cartesian coordinate equation of line l;
(2) If line l intersects curve C at points A and B, find the maximum area of △ABM.

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