
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 discrete random variable $X$ is given by $P({X=k})=\frac{a}{{k({k+1})}}$, $k=1$, $2$, $3$, $4$, $5$, $6$, where $a$ is a constant. Find $P({\frac{1}{2}＜X＜4})$.

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