
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

A random variable \( X \) is defined by the distribution function

$$
F(x)=\left\{\begin{array}{lc}
0 & \text{if } x \leq 0 \\
x / 2 & \text{if } 0 < x \leq 2 \\
1 & \text{if } x > 2
\end{array}\right.
$$

Find the probability that, as a result of the trial, the random variable \( X \) takes a value in the interval \( (1,2) \).

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