
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 random variable $X$ as follows:

| $X$ | $2$ | $3$ | $6$ |
|-----|-----|-----|-----|
| $P$ | $\frac{1}{2}$ | $a$ | $\frac{1}{6}$ |

If the random variable $Y$ satisfies $Y=4X+3$, then $D\left(Y\right)=\_\_\_\_\_\_$.

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