
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]


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Parametric Equations and Polar Coordinates

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

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