
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 random variable $X$ follows the Simpson's law (the law of the isosceles triangle) on the interval $x \in [-c, c]$. Find:

a) the probability density function of this random variable;

b) the probability that the variable $X$ falls within the interval $(c / 2, c)$.

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