
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 distribution of the random variable $\xi$ is $P(\xi=x)= \dfrac{xk}{15}$, where $x$ takes values $(1,2,3,4,5)$, find the value of $P\left( \left. \dfrac{1}{2} < \xi < \dfrac{5}{2} \right. \right)$.

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