
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 a discrete random variable $X$ as follows:

| $x$ | $-1$ | $0$ | $1$ | $2$ |
|-----|-----|-----|-----|-----|
| $P$ | $a$ | $b$ | $c$ | $\frac{1}{3}$ |

If $E(X)=\frac{3}{4}$ and $P(X\geq1)=\frac{7}{12}$, calculate the variance of $X$.

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