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

| $\xi$ | $-1$ | $0$ | $1$ |
|-------|------|-----|-----|
| $P$   | $a$  | $b$ | $c$ |

where $a$, $b$, and $c$ form an arithmetic sequence. If $E\xi = \frac{1}{3}$, then the value of $D\xi$ is ____.

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