
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 integers \( A \) and \( B \) be such that 
\[
\frac{A}{x+6} + \frac{B}{x^2-5x} = \frac{x^3 - 3x^2 + 12}{x^3 + x^2 - 30x}
\]
for all values of \( x \) except for \( -6 \), \( 0 \), and \( 5 \). Find \( \frac{B}{A} \).

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