
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 is $\rho=1$, with the pole as the origin and the positive half-axis of the x-axis as the polar axis, a Cartesian coordinate system is established. The parametric equation of line $l$ is $$\begin{cases} x=1+ \frac {t}{2} \\ y=2+ \frac { \sqrt {3}}{2}t \end{cases} (t \text{ is the parameter}).$$  
(1) Write the Cartesian coordinate equations of line $l$ and curve $C$;  
(2) Suppose curve $C$ undergoes a scaling transformation $$\begin{cases} x'=2x \\ y'=y \end{cases}$$ to obtain curve $C'$, and let any point on curve $C'$ be $M(x, y)$, find the minimum value of $$x+2 \sqrt {3}y.$$

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