
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
A square is inscribed in a circle of radius 1. An isosceles triangle is inscribed in the square. What is the ratio of the area of this triangle to the area of the shaded region?
A $\pi: \sqrt{2}$
B $\pi: 1$
C $1: 4$
D $1: \pi-2$
E $2: \pi$

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