
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 diagram shows an isosceles right-angled triangle with a hypotenuse of length \( y \). The interior of the triangle is split into identical squares and congruent isosceles right-angled triangles. What is the total shaded area inside the triangle?

A) \( \frac{y^{2}}{2} \)  
B) \( \frac{y^{2}}{4} \)  
C) \( \frac{y^{2}}{8} \)  
D) \( \frac{y^{2}}{16} \)  
E) \( \frac{y^{2}}{32} \)

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