
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 ellipse $C: \frac{x^2}{4} + \frac{y^2}{3} = 1$, and the line $l: \begin{cases} x=-3+ \sqrt {3}t \\ y=2 \sqrt {3}+t \end{cases}$ ($t$ is a parameter).

(1) Write the parametric equation for the ellipse $C$ and the general equation for the line $l$;

(2) Let $A(1,0)$, if point $P$ on ellipse $C$ satisfies that the distance to point $A$ is $\frac{3}{2}$, find the coordinates of point $P$.

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