
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 Cartesian coordinate system $xOy$, the parametric equation of curve $C$ is $\begin{cases} & x=2\sqrt{3}\cos a \\ & y=2\sin a \end{cases}$, where $a$ is a parameter and $a \in (0, \pi)$. In the polar coordinate system with the origin $O$ as the pole and the positive half axis of $x$ as the polar axis, the polar coordinates of point $P$ are $(4\sqrt{2}, \frac{\pi}{4})$, and the polar equation of line $l$ is $\rho \sin(\theta - \frac{\pi}{4}) + 5\sqrt{2} = 0$.

(1) Find the Cartesian equation of line $l$ and the general equation of curve $C$.

(2) Suppose $Q$ is a moving point on curve $C$, and $M$ is the midpoint of segment $PQ$. Find the maximum distance from point $M$ to the line $l$.

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