
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
The partial fraction decomposition of
\[\frac{x^2 + 5x - 14}{x^3 - 4x^2 + x + 6}\]
is
\[\frac{P}{x - 3} + \frac{Q}{x + 1} + \frac{R}{x - 2}.\]
Find the sum \(P + Q + R.\)

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