
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 \( A, B, \) and \( C \) be constants such that the equation 
\[
\frac{(x+B)(Ax+42)}{(x+C)(x+9)} = 3
\]
has infinitely many solutions for \( x \). For these values of \( A, B, \) and \( C \), determine how many values of \( x \) are not solutions to the equation, and find their sum.

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