
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
Given the probability distribution of the random variable $X$ is $P(X=n)= \dfrac{a}{n(n+1)}(n=1,2,3,4)$, where $a$ is a constant, find the value of $P\left( \left. \dfrac{1}{2} < X < \dfrac{5}{2} \right. \right)$.

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