
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 strange die is rolled. It can land on numbers 1 through 6. If it lands on 1 or 2, you win 2 dollars. If it lands on 3 or 4, you win 5 dollars. If it lands on 5, you lose 4 dollars. If it lands on 6, you lose 2 dollars. What is the expected winnings from rolling this die?

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