
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 a cylinder with a base radius of $r$ and height of $h$, where $h < 2πr$, the side surface when unfolded forms a rectangle whose length is twice its width. What is the ratio of the total surface area to the lateral (side) surface area of this cylinder?

A) $\dfrac {1+π}{π}$
B) $\dfrac {1+2π}{π}$
C) $\dfrac {1+2π}{2π}$
D) $\dfrac {1+4π}{2π}$

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