
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
Let a random experiment have only two outcomes: $A$ and $\overline{A}$, with $P(A)=p$. Define the random variable $X$ as follows:
$$
X= \begin{cases} 
1, & \text{if } A \text{ occurs} \\
0, & \text{if } A \text{ does not occur}
\end{cases}
$$
Calculate the variance of $X$.

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