
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 on the entire \( O x \) axis by the distribution function \( F(x) = \frac{1}{2} + \frac{1}{\pi} \operatorname{arctg}\left( \frac{x}{2} \right) \). Find a possible value of \( x_1 \) that satisfies the following condition: with a probability of \( \frac{1}{4} \), the random variable \( X \) will take on a value greater than \( x_i \) as a result of the trial.

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