
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
Find the probability that the random variable \(X\) falls within the interval \((0, 1)\), given the cumulative distribution function (CDF):

\[ 
F(x) = \begin{cases} 
0 & \text{if } x < 0, \\
\frac{x}{2} & \text{if } 0 \leq x \leq 2, \\
1 & \text{if } x > 2.
\end{cases} 
\]

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