
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 we roll two dice and flip two coins: a nickel and a quarter. What is the probability that the total value of the coins showing heads plus the sum of the numbers on the dice is at least 12?

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