
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
Yannick is playing a game with 100 rounds, starting with 1 coin. During each round, there is an \( n \% \) chance that he gains an extra coin, where \( n \) is the number of coins he has at the beginning of the round. What is the expected number of coins he will have at the end of the game?

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