
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
Consider four parallel lines on the plane. Let these be $a, b, c,$ and $d$ in order. It is known that the distance between $a$ and $b$ is 1, the distance between $b$ and $c$ is 3, and the distance between $c$ and $d$ is also 1. Consider all rectangles with vertices lying on exactly one of these lines. How can we obtain the rectangle with the smallest possible area, and what is this area?

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