
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 that the non-zero constant $d$ is the common difference of the arithmetic sequence $x\_1$, $x\_2$, $...$, $x\_{19}$, and the random variable $ξ$ can take the values $x\_1$, $x\_2$, $...$, $x\_{19}$ with equal probability, then the variance $Dξ=$ \_\_\_\_\_\_.

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