
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
Jamie encountered a challenging trigonometry problem during their study session. The problem involved calculating particular values associated with the roots of a quadratic equation \[x^2 - tx + q,\] where the roots \(r_1\) and \( r_2\) satisfy \(r_1 + r_2 = r_1^2 + r_2^2 = \cdots = r_1^{10} + r_2^{10}.\) Jamie decides to determine the maximum possible value of \[\dfrac{1}{r_1^{10}} + \dfrac{1}{r_2^{10}}.\]

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