
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
In the graph of \(\frac{x^2 - 2x + 1}{x^3 - 3x^2 + 2x}\), let \(a\) be the number of holes in the graph, \(b\) be the number of vertical asymptotes, \(c\) be the number of horizontal asymptotes, and \(d\) be the number of oblique asymptotes. Calculate \(a^2+2b^2+3c^2+4d^2\).

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