
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 polynomial 
\[8x^5 - b_4 x^4 + b_3 x^3 + b_2 x^2 + b_1 x + 20 = 0.\]
Find the number of different possible rational roots of this polynomial.

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