
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 curve C is $\rho = \sqrt{3}$, and the parametric equations of line l are $x = 1 + \frac{\sqrt{2}}{2}t$, $y = \frac{\sqrt{2}}{2}t$ (where t is the parameter), and the parametric equations of curve M are $x = \cos \theta$, $y = \sqrt{3} \sin \theta$ (where $\theta$ is the parameter).
1. Write the Cartesian coordinate equation for curve C and line l.
2. If line l intersects curve C at points A and B, and P is a moving point on curve M, find the maximum area of triangle ABP.

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