
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

3. The remaining 60% of the voters do not want to see any of the candidates as their representative, but under equal conditions, they are willing to sell their votes for money to the candidate who offers them the most.

It is known that if any candidate offers 1 monetary unit per voter, he will gain one additional supporter; if he offers 2 monetary units, he will gain two additional supporters, and so on. Voting in country Y is open, so only after the election will a candidate know exactly who voted for him, and he will pay the voters immediately after they vote. It is also known that there are only two candidates in the election, all voters are required to vote without spoiling the ballots, i.e., each of the twenty-five voters must vote for either Ratibor or Nikifor, or against all, and the candidates themselves are not allowed to vote. Additionally, Ratibor (like Nikifor) may compete unfairly, but he is not wealthy, so the maximum amount of money he is willing to spend on bribing voters is just enough to win the election if the opponent acts honestly. Nikifor is aware of Ratibor's position and potential expenses, so he is always willing to pay more than Ratibor would offer to bribe any voter. To win the election, any candidate must secure at least 50% of the votes. Monetary units in this country can only have integer values.

(a) Write out the function that describes the offer of votes for any of the candidates.

(b) Find the minimum expenses that Nikifor would incur to bribe voters and win the election, assuming he knows for certain that Ratibor will compete dishonestly, and even after the election, neither candidate can determine which group each voter belonged to.

(c) Nikifor has found a way to reliably determine before the election the minimum amount of money each voter is willing to accept for selling their vote, and now the candidate can individually negotiate with all the voters he needs. It is known that voters keep their word: if after negotiating with Nikifor, Ratibor approaches them, none of them will change their decision to vote for Nikifor, no matter how much Ratibor offers them for their vote. The cost of information about an individual voter is given by F monetary units. What is the maximum amount F that Nikifor is willing to pay for such information to win the election?

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