
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
Jenny considers the quadratic equation $x^2 - sx + p$ with roots $r_1$ and $r_2$. She finds out that all power sums of the roots up to 2023 equate to $s$, i.e., $r_1 + r_2 = r_1^2 + r_2^2 = \cdots = r_1^{2023} + r_2^{2023} = s$. Jenny is curious to find out the maximum possible value of $\frac1{r_1^{2024}}+\frac1{r_2^{2024}}$.

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