
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 $f(x) = Ax + B + C$ and $g(x) = Bx + A - C$, where $A \neq B$, $A + B \neq 0$ and $C$ is a non-zero constant. If $f(g(x)) - g(f(x)) = 2C$, what is the value of $A + B + 2C$?

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