
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
Let \( x, y, z \) be nonnegative real numbers. Define
\begin{align*}
C &= \sqrt{x + 3} + \sqrt{y + 6} + \sqrt{z + 11}, \\
D &= \sqrt{x + 2} + \sqrt{y + 4} + \sqrt{z + 9}.
\end{align*}
Find the minimum value of \( C^2 - D^2 \).

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