
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
Determine \( A, B \), and \( C \) such that for all permissible values of \( x \) the equality holds:

\[ \frac{x^{2}+5}{x^{3}-3 x+2}=\frac{A}{x+2}+\frac{B}{(x-1)^{2}}+\frac{C}{x-1}. \]

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