
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 the distribution of the random variable $X$ as shown below:

| $X$ | $0$ | $1$ | $2$ |
|-----|-----|-----|-----|
| $P$ | $0.4$ | $p$ | $0.4$ |

Find the value of $p$ and $D(X)$.

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