
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 a quadrilateral inscribed in a rectangle such that two sides of the quadrilateral are sides of the rectangle, and opposite vertices of the quadrilateral are connected by a diagonal that is also the rectangle's diagonal. Given that the rectangle's length is twice its width, and the diagonal measures 10 units, calculate the perimeter of the quadrilateral.

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