
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*}
A &= \sqrt{x + 3} + \sqrt{y + 4} + \sqrt{z + 7}, \\
B &= \sqrt{x + 2} + \sqrt{y + 2} + \sqrt{z + 2}.
\end{align*}
Find the minimum value of $A^2 - B^2.$

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