
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 bag contains 10 red, 12 green, 15 yellow, 18 blue, and 5 purple jelly beans. A jelly bean is selected at random. What is the probability that it is purple? Additionally, what is the probability that the jelly bean is either blue or purple?

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