
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 parametric equation of curve $C_1$ as $\begin{cases} x=1+\sqrt{2}\cos t, \\ y=\sqrt{2}\sin t, \end{cases}$ (with $t$ as the parameter), and curve $C_2$ with the polar coordinate equation $2\rho \cos \theta - \rho \sin \theta - 4 = 0$.

(I) Convert the parametric equation of curve $C_1$ into a standard form, and convert the polar coordinate equation of curve $C_2$ into a rectangular coordinate equation, and identify the type of each curve.

(II) Determine whether curves $C_1$ and $C_2$ have two distinct common points. If they do, find the distance between these two points. If they don't, provide a reason.

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