
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

A society of \(n\) members is selecting one representative from among themselves.

a) In how many ways can an open vote occur if each member votes for one person (possibly themselves)?

b) Solve the same problem if the vote is secret, i.e., only the number of votes each candidate receives is considered, and it does not matter who voted for whom.

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