
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
For positive real numbers $x$ and $y$, define a new operation $x \diamond y = \frac{x^2 + y^2}{x+y}$. Suppose $w, x, y,$ and $z$ are positive real numbers satisfying $x + y + z + w = 10$. Evaluate the expression $w \diamond x \diamond y \diamond z$.
A) $\frac{x^2 + y^2 + z^2 + w^2 + x + y + z + w}{20}$
B) $\frac{x^2 + y^2 + z^2 + w^2}{20}$
C) $\frac{x^2 + y^2 + z^2 + w^2}{10}$
D) $\frac{x^2 + y^2 + z^2 + w^2 + x + y + z + w}{10}$

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