
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
The polynomial equation \[x^4 - 9x^3 + bx^2 + cx + d = 0,\] where \( b, c, \) and \( d \) are rational numbers, has roots \( 5 - \sqrt{21} \) and \( 5 + \sqrt{21} \). If another root is an integer which is the immediate next integer following a factor of 20, determine what the last root is.

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