
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
Let non-zero constant $d$ be the common difference of the arithmetic sequence $x_1$, $x_2$, $x_3$, ..., $x_9$. The random variable $\xi$ takes on the values $x_1$, $x_2$, $x_3$, ..., $x_9$ with equal probability. Find the variance $D\xi$.

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