
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
Suppose a die is rolled. There are two opportunities to roll: you can choose to roll just once, or twice, but the result is determined by the last roll. What is the expected value of the outcome in this scenario? If there are three opportunities, still taking the value of the last roll, what is the expected value of the outcome?

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