
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 a straight line l with the polar equation $\rho\sin(\frac{\pi}{4}-\theta) = \sqrt{2}$, and a circle M with the parametric equations $\begin{cases} x = 1 + 3\cos\theta \\ y = -2 + 3\sin\theta \end{cases}$ (where $\theta$ is the parameter).  
(1) Convert the polar equation of the straight line to a Cartesian coordinate equation;  
(2) If the straight line l intersects the circle M at points A and B, find the sum of the slopes of lines AM and BM.

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