
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 equations for curves $C_1$ and $C_2$ are respectively given by 
$$
\begin{cases}
x=t \\
y= \sqrt{t}
\end{cases}
\quad \text{(where $t$ is the parameter)}
$$
and 
$$
\begin{cases}
x= \sqrt{2}\cos\theta \\
y= \sqrt{2}\sin\theta
\end{cases}
\quad \text{(where $\theta$ is the parameter)}.
$$
Find the coordinates of the intersection point(s) of curves $C_1$ and $C_2$.

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