
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 rectangular coordinate system, with the coordinate origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis, the polar coordinates of point $M$ are $(2\sqrt{2}, \frac{\pi}{4})$. The parameter equation of curve $C$ is $\begin{cases} x=1+2\cos\alpha \\ y=2\sin\alpha \end{cases}$ ($\alpha$ is the parameter).
(1) Line $l$ passes through $M$ and is tangent to curve $C$. Find the polar coordinate equation of line $l$.
(2) Point $N$ is symmetric to point $M$ about the $y$-axis. Find the range of distances from points on curve $C$ to point $N$.

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