
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 polar coordinate equation of curve $C$ is $ρ=1$, a rectangular coordinate system is established with the pole as the origin and the positive half of the polar axis as the axis. Curve $C$ undergoes a stretching transformation $\begin{cases} \overset{\ }{x}=3x \\ \overset{\ }{y}=y\end{cases}$ to obtain curve $C'$. Let $M(x,y)$ be any point on curve $C'$. Find the minimum value of $x+2 \sqrt{3}y$.

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