
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
a) Given the quadratic equation \(x^{2} - 9x - 10 = 0\). Let \(a\) be its smallest root. Find \(a^{4} - 909a\).

b) For the quadratic equation \(x^{2} - 9x + 10 = 0\), where \(b\) is the smallest root, find \(b^{4} - 549b\).

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