
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
The distribution function of the random variable \(X\) is given by

$$
F(x)= \begin{cases}0 & \text{if } x \leq 0 \\ \frac{x^{2}}{1+x^{2}} & \text{if } x > 0\end{cases}
$$

Find its probability density function.

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