
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
Consider the function given by the expression $\frac{x^2 - 4x + 4}{x^3 - 2x^2 - x + 2}$. Determine the number of holes ($a$), vertical asymptotes ($b$), horizontal asymptotes ($c$), and oblique asymptotes ($d$) in the graph of the function. Finally, calculate $a + 2b + 3c + 4d$.

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