
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
Five dice are rolled simultaneously. Such a simultaneous roll of multiple dice is called a salvo. Dice that show sixes are set aside. The remaining dice are rolled again - another salvo. Those that do not show sixes on the second roll are rolled again, and so on, until all the dice show sixes.

a) Find the expected total number of dice rolled.

b) Find the expected total number of points rolled by the time all the dice show sixes.

c) Find the expected number of salvos.

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