
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
In trapezoid $ABCD$, sides $AB$ and $CD$ are parallel with $AB = 2x$ and $CD = 4x$ where $x$ is a non-zero real number, and side $AD$ is twice the length of side $BC$. If side $BC = y$, determine the perimeter of trapezoid $ABCD$ in terms of $x$ and $y$.

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