
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 discrete random variable $X$ with the probability mass function $P({X=\frac{k}{5}})=ak$ for $k=1,2,3,4,5$, calculate $P({\frac{1}{{10}}＜X＜\frac{3}{5}})$.

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