
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 postman needs to deliver mail on a street with $n$ houses. Each day, he goes to the post office, collects the mail for residents of one house, delivers it, and then returns to the post office to collect mail for the next house. This process continues until he has delivered mail to all houses. Where should the post office be located so that the total distance the postman travels is minimized, assuming the street is a straight line segment?

a) Solve the problem for $n=5$.

b) Solve the problem for $n=6$.

c) Solve the problem for an arbitrary $n$.

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