
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 list of the random variable $X$, $P(X=\frac{k}{5})=ak$, where $k=1,2,3,4,5$.

1. Find the value of the constant $a$.
2. Find $P(X\geqslant \frac{3}{5})$.
3. Find $P(\frac{1}{10} < X < \frac{7}{10})$.

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