
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 plane rectangular coordinate system $(xOy)$, with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, establish a polar coordinate system. The polar coordinate equation of the curve $C_{1}$ is $ρ=4\cos θ$, and the parametric equation of the line $l$ is $ \begin{cases} x=1- \frac {2 \sqrt {5}}{5}t \\ y=1+ \frac { \sqrt {5}}{5}t\end{cases}(t\text{ is the parameter})\text{.}$

(1) Find the rectangular coordinate equation of curve $C_{1}$ and the normal equation of line $l$.
(2) If the parametric equation of curve $C_{2}$ is $ \begin{cases} \overset{x=2\cos α }{y=\sin α }\end{cases}(α\text{ is the parameter})\text{,}$ and the polar angle of point $P$ on curve $C_{1}$ is $ \frac {π}{4}$, $Q$ is a moving point on curve $C_{2}$, find the maximum value of the distance from the midpoint $M$ of $PQ$ to line $l$.

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