
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 circle is circumscribed around a triangle with sides $8, 15,$ and $17$. Inside the circle but outside the triangle, three regions are formed. Let $X$ and $Y$ be the areas of the two smaller regions, and let $Z$ be the area of the largest region. Find the ratio $\frac{X+Y}{Z}$.
A) 0.431
B) 0.471
C) 0.571
D) 0.671

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