
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
(1) Convert the decimal number $23$ to binary.

(2) If selecting $3$ representatives from four people named A, B, C, and D, the probability of A being selected is ______.

(3) Given real numbers $x$ and $y$ satisfy the system of inequalities:
\[
\begin{cases}
x - y - 2 \leqslant 0 \\
x + 2y - 5 \geqslant 0 \\
y - 2 \leqslant 0
\end{cases}
\]
The range of values for $z = \frac{y}{x}$ is ______.

(4) The coordinates of the point symmetric to $(0,2)$ with respect to the line $l: x + y - 1 = 0$ are ______.

(5) Given the average of some $8$ data points is $5$ and the variance is $3$. If another data point, $5$, is added, the variance of these $9$ data points is ______.

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