
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 $xOy$, 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 $\rho(\sin\theta + \cos\theta) = 1$, and the parametric equation of curve $C_2$ is given by:
$$
\begin{cases}
x = 2\cos\theta \\
y = \sin\theta
\end{cases}
$$
where $\theta$ is the parameter.
(I) Find the Cartesian equation of curve $C_1$ and the general equation of curve $C_2$.
(II) Determine whether curves $C_1$ and $C_2$ have two intersection points. If they do, calculate the distance between the two points; if not, explain why.

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