
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 in the Cartesian coordinate system xOy, with the origin O as the pole and the positive x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C_1$ is $\rho=4\cos\theta$, and the parametric equation of line $l$ is $$\begin{cases} x=1- \frac {2 \sqrt {5}}{5}t \\ y=1+ \frac { \sqrt {5}}{5}t \end{cases}$$ (t is the parameter).
(1) Find the Cartesian equation of curve $C_1$ and the general equation of line $l$;
(2) If the parametric equation of curve $C_2$ is $$\begin{cases} x=2\cos\alpha \\ y=\sin\alpha \end{cases}$$ ($\alpha$ is the parameter), and the polar angle of point P on curve $C_1$ is $\frac {\pi}{4}$, Q is a moving point on curve $C_2$, find the maximum distance from the midpoint M of PQ to line $l$.

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