
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 a quadratic polynomial \[x^2 - tx + q,\] where the roots \(r_1\) and \(r_2\) satisfy \[r_1 + r_2 = r_1^2 + r_2^2 = r_1^4 + r_2^4.\] Determine the minimum possible value of \[\dfrac{1}{r_1^5} + \dfrac{1}{r_2^5}.\]

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