
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
I have two 20-sided dice: one die has 3 maroon sides, 9 teal sides, 7 cyan sides, and one sparkly side; the other die has 5 maroon sides, 6 teal sides, 8 cyan sides, and one sparkly side. I also roll a fair 6-sided die along with these dice. What is the probability that both 20-sided dice show the same color, and the 6-sided die shows a number greater than 4?

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