
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 that the pole of the polar coordinate system coincides with the origin of the Cartesian coordinate system, and the polar axis overlaps with the positive half of the x-axis, the polar equation of curve C is $\rho^2\cos^2\theta + 3\rho^2\sin^2\theta = 3$. The parametric equation of line l is 
$$
\begin{cases}
x=-\sqrt{3}t \\
y=1+t
\end{cases}
(t\text{ is the parameter, } t\in\mathbb{R}).
$$
Find a point M on curve C such that the distance from M to the line l is maximized.

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