
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
Examining the properties of the roots of the function $x^2 - tx + q$, where the roots $r_1$ and $r_2$ satisfy the condition that $r_1 + r_2 = r_1^2 + r_2^2 = \dots = r_1^{2010} + r_2^{2010}$. Calculate the maximum possible value of $\dfrac1{r_1^{2010}}+\dfrac1{r_2^{2010}}$.

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