
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
Vasya throws three dice (each die has numbers from 1 to 6 on its faces) and sums up the rolled numbers. Furthermore, if all three rolled numbers are different, he can roll all three dice again and add the rolled numbers to the already accumulated sum. This process continues until at least two of the three rolled numbers are the same. What is the expected value of Vasya's total result?

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