
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 distribution of the random variable $\xi$ is as follows:

| $\xi$ | $0$   | $1$              | $2$       |
|-------|-------|------------------|-----------|
| $P$   | $a$   | $2a-\frac{1}{6}$ | $\frac{1}{6}$ |

Determine $D(\eta)$ where $\eta = 2\xi - 1$.

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