
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
Dave has a pile of fair standard six-sided dice. In round one, Dave selects eight of the dice and rolls them. He calculates the sum of the numbers face up on those dice to get  $r_1$ . In round two, Dave selects  $r_1$  dice and rolls them. He calculates the sum of the numbers face up on those dice to get  $r_2$ . In round three, Dave selects  $r_2$  dice and rolls them. He calculates the sum of the numbers face up on those dice to get  $r_3$ . Find the expected value of  $r_3$ .

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