
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
Let  $a,b,c$  be the roots of the polynomial  $x^3 - 20x^2 + 22.$  Find \[\frac{bc}{a^2}+\frac{ac}{b^2}+\frac{ab}{c^2}.\]

*Proposed by Deyuan Li and Andrew Milas*

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