
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
Monica is now playing a different game involving two fair 6-sided dice. She wins $4 times the sum of the two dice if the total is odd. If the total is even, she wins nothing unless both numbers rolled are identical (doubles), in which case she wins $2 times the sum of the two dice. Otherwise, she loses $6. What is the expected value of her winnings on one roll of two dice? Express your answer as a dollar value to the nearest cent.

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