
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 two discrete random variables $\xi$ and $\eta$, where $\eta = 3\xi + 1$, and the distribution of $\xi$ is as follows:

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

When $E(\xi) = \frac{2}{3}$, find $D(\eta)$.

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