
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 $(xOy)$, curve $C_1: x^2 + y^2 = 1$ undergoes a transformation defined by the system of equations $\begin{cases} x^2 = 2x \\ y^2 = y \end{cases}$, resulting in curve $C_2$. In the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of curve $C_3$ is given by $\rho = \frac{-8}{\rho - 6\sin\theta}$.

(1) Find the parametric equations of curve $C_2$ and the rectangular equation of curve $C_3$.
(2) Let $M$ be a point on curve $C_2$, and let a tangent line be drawn from $M$ to curve $C_3$, touching it at point $N$. Find the maximum value of $|MN|$.

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