
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
Given $10≤x_{1}<x_{2}<x_{3}<x_{4}≤10^{4}$, $x_{5}=10^{5}$. The probabilities of the random variable $\xi_{1}$ taking values $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$ are all $0.2$, and the probabilities of the random variable $\xi_{2}$ taking values $\frac{x_{1}+x_{2}}{2}$, $\frac{x_{2}+x_{3}}{2}$, $\frac{x_{3}+x_{4}}{2}$, $\frac{x_{4}+x_{5}}{2}$, $\frac{x_{5}+x_{1}}{2}$ are also $0.2$. Determine the relationship between $D\xi_{1}$ and $D\xi_{2}$.

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