
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 $ABCD$, with bases $AB$ and $CD$, side $AB$ is of length $10$ units, and the length of side $CD$ is twice the length of $AB$. Additionally, non-base sides $AD$ and $BC$ are equal to each other. Determine the length of $AD$ if the perimeter of $ABCD$ equals $42$ units.

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