
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 polar equation of a line is $\rho\cos\theta + \rho\sin\theta - 1 = 0$. Taking the pole as the origin of the Cartesian coordinate system, and the polar axis as the positive half of the x-axis, establish a Cartesian coordinate system. On curve $C: \begin{cases} x=-1+\cos\theta \\ y=\sin\theta \end{cases}$ (where $\theta$ is the parameter), find a point such that its distance to the line is minimized, and determine the coordinates of this point and the minimum distance.

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