
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
The base of a quadrilateral pyramid \( ABCD \) is a trapezoid where \( AB = BC = CD = \frac{1}{2} AD \). The foot of the pyramid's height is at the intersection of the base's diagonals, and the edges starting from vertices \( A \) and \( C \) to the apex of the pyramid form right angles. What are the surface area and volume of the pyramid?

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