
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 probability distribution of the random variable $X$ is given by $P(X=k) = \frac{c}{k(k+1)}$, where $k=1,2,3,4$, and $c$ is a constant. Find the value of $P\left(\frac{1}{2} < X < \frac{5}{2}\right)$.

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