
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 \( X \) in the interval \( (2, 4) \) is defined by the probability density function \( f(x) = -\frac{3}{4} x^2 + \frac{9}{2} x - 6 \); outside this interval, \( f(x) = 0 \). Find the mode, expected value, and median of the variable \( X \).

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