
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
To join a club, each new member must pay an entry fee to each existing member equal to the total amount the existing member paid when they joined, plus one euro. If the first member paid one euro, how much will the $n$-th member have to pay in total?

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