
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 the polar equation of curve C is $\rho^2 - 2\sqrt{2}\rho\cos(\theta + \frac{\pi}{4}) - 2 = 0$, with the pole as the origin of the Cartesian coordinate system and the polar axis as the positive x-axis, establish the Cartesian coordinate system xOy.
1. If line l passes through the origin and the chord cut by curve C has the minimum length, find the equation of line l in Cartesian coordinates.
2. If M is a moving point on curve C, and the Cartesian coordinates of point M are $(x, y)$, find the maximum value of $x+y$.

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