
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
Triangle XYZ is a right triangle with ∠XYZ as its right angle, m∠YXZ = 45°, and XY = 12. Let P be a point randomly chosen inside XYZ, and extend YP to meet XZ at D. What is the ratio of the area of the trapezoid XYZD to the area of triangle XYZ?

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