
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
Let the random variable $X$ have the probability distribution $P(X= \frac {k}{5})=ak$ for $k=1,2,3,4,5$.

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

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