
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
Johann has 100 biased coins, each with a probability of $\frac{1}{3}$ of landing heads. He flips all the coins. All coins that land tails are tossed again, allowing up to four flips in total for each coin. What is the expected number of coins that show heads after all flips?
A) 65
B) 80
C) 50
D) $\frac{6500}{81}$

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