
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 $(xOy)$, there are two curves $C_{1}$: $ \begin{cases} x=2\sin \theta \\ y=a\cos \theta \end{cases} (\theta$ is the parameter, $a > 0$) and $C_{2}$: $ \begin{cases} x=t+1 \\ y=2-2t \end{cases} (t$ is the parameter$)$ .
(I) If the two curves have a common point on the $y$-axis, find the value of $a$;
(II) When $a=2$, determine the number of intersection points between the two curves.

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