
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
Toss a fair coin $n$ times ($3 \leq n \leq 8$), the number of times the coin lands heads up, $\xi$, follows a binomial distribution $B(n, \frac{1}{2})$. If $P(\xi=1) = \frac{3}{32}$, then the variance $D(\xi) = \_\_\_\_\_\_$.

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