
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 curve C as $\rho=2$, establish a Cartesian coordinate system with the pole as the origin and the positive x-axis as the polar axis. The parametric equation for line L is $\begin{cases} x=1+t \\ y=2+\sqrt{3}t \end{cases}$ (with $t$ as the parameter).
(1) Write down the general equation of line L and the Cartesian coordinate equation of curve C;
(2) Suppose curve C undergoes a scaling transformation $\begin{cases} x'=x \\ y'=\frac{1}{2}y \end{cases}$ to obtain curve C′. Let M($x$, $y$) be any point on C′, find the minimum value of $x^2 - \sqrt{3}xy + 2y^2$ and find the coordinates of the corresponding point M.

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