
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 line $l$: $\begin{cases} x=1+t \\ y=3-2t \end{cases}$ (where $t$ is a parameter and $t \in \mathbb{R}$) and the curve $C$: $\begin{cases} x=\cos \alpha \\ y=2+\cos 2\alpha \end{cases}$ (where $\alpha$ is a parameter and $\alpha \in [0,2\pi))$, find the coordinates of the intersection point(s) between line $l$ and curve $C$.

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