
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 real numbers $x$ and $y$, define the operation $x \diamond y = \sqrt{x^2 + y^2 + xy}$. What is the value of $(6 \diamond 15) \diamond ((-15) \diamond (-6))$?
A) $351$
B) $351\sqrt{2}$
C) $351\sqrt{3}$
D) $\sqrt{702}$
E) $702$

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