
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
Suppose the probability distribution of the random variable $X$ is given by $P\left(X=\frac{k}{5}\right)=ak$, where $k=1,2,3,4,5$.
(1) Find the value of $a$.
(2) Calculate $P\left(X \geq \frac{3}{5}\right)$.
(3) Find $P\left(\frac{1}{10} < X \leq \frac{7}{10}\right)$.

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