
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 $f(x) = Ax^2 + B$ and $g(x) = Bx^2 + A$, where $A \neq B$. Calculate $A + B$ given that $f(g(x)) - g(f(x)) = -A^2 + B^2$.

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