
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
A point is chosen randomly on the number line between 0 and 1, and this point is colored green. Then, another point is chosen randomly on the number line between 0 and 1, and this point is colored purple. Determine the probability that the number of the purple point is more than $\frac{3}{4}$ times the number of the green point and less than $1.5$ times the number of the green point.

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