
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 the values of \(A, B, C\) if

$$
\frac{(x+1)^{2}}{(x+2)\left(x^{2}+x+1\right)} \equiv \frac{A}{x+2}+\frac{B x+C}{x^{2}+x+1}
$$

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