
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 $xOy$, the parametric equation of line $l$ is $\begin{cases} x= \frac { \sqrt {2}}{2}t- \sqrt {2} \\ y= \frac { \sqrt {2}}{4}t\end{cases}$ (where $t$ is the parameter), and the parametric equation of ellipse $C$ is $\begin{cases} x=\cos \theta \\ y= \frac {1}{2}\sin \theta\end{cases}$ (where $\theta$ is the parameter). Find the coordinates of the intersection point(s) between line $l$ and ellipse $C$.

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