
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
Three points are chosen at random on the number line between 0 and 1. The first point is colored green, the second purple, and the third red. What is the probability that the number of the purple point is greater than the number of the green point but less than four times the number of the green point, and also greater than the red point?

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