
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
Find constants \(A\), \(B\), and \(C\) such that
\[
\frac{5x}{(x - 4)(x - 2)^2} = \frac{A}{x - 4} + \frac{B}{x - 2} + \frac{C}{(x - 2)^2}.
\]

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