
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 of line $l$ are given by $\begin{cases} x = t + 1, \\ y = 2t \end{cases} (t \text{ is the parameter})$, and the parametric equations of curve $C$ are given by $\begin{cases} x = 2 \tan^2 \theta, \\ y = 2 \tan \theta \end{cases} (\theta \text{ is the parameter})$. Find the Cartesian equations of line $l$ and curve $C$, and determine the coordinates of their intersection point(s).

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