
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, the ordinary equation of curve $C_1$ is $\frac{x^2}{16} + \frac{y^2}{8} = 1$. Establish a polar coordinate system with the origin as the pole, the positive half of the $x$-axis as the polar axis, and the same unit of length as the rectangular coordinate system. The polar equation of curve $C_2$ is $\rho^2 + 2\rho \cos \theta - 1 = 0$.
(I) Find the parametric equations of curves $C_1$ and $C_2$;
(II) If point $M$ is on curve $C_1$ and point $N$ is the center of curve $C_2$, find the minimum value of $|MN|$.

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