
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 \[\frac{(x+B)(Ax+36)}{(x+C)(x+9)} = 3\]has infinitely many solutions for \(x\). For these values of \(A\), \(B\), and \(C\), it turns out that there are only finitely many values of \(x\) which are not solutions to the equation. Find the sum of these values of \(x\).

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