
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
Paul tosses a fair 8-sided die. If the roll is a prime number, then he wins that amount in dollars. If the roll is composite, he wins nothing unless he rolls the highest composite number on the die, in which case he loses twice that amount in dollars. Otherwise, he gains 2 dollars. What is the expected value of his winnings on one die toss? Express your answer as a dollar value to the nearest cent.

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