
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 $\xi$ is given by $P(\xi=k)= \frac{c}{k(k+1)}$, where $k=1, 2, 3, 4$, and $c$ is a constant. Find the value of $P(\frac{1}{2} < \xi < \frac{5}{2})$.

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