
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 constants $P$, $Q$, and $R$ such that
$$\frac{-2x^2 + 5x - 7}{x^3 - x} = \frac{P}{x} + \frac{Qx + R}{x^2 - 1}$$
and provide your answer as the ordered triplet $(P, Q, R)$.

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