
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 $f(x) = Ax^2 - 4B^2 x + C$ and $g(x) = Bx + 1$, where $B \neq 0$ and $C \neq 0$. If $f(g(2)) = 0$, what is $A$ in terms of $B$ and $C$?

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