
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 \( p, q, r \) be nonnegative real numbers. Define:
\[
A = \sqrt{p + 3} + \sqrt{q + 6} + \sqrt{r + 12}, \quad B = \sqrt{p + 2} + \sqrt{q + 2} + \sqrt{r + 2}.
\]
Find the minimum value of \( A^2 - B^2 \).

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