
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 street has $n$ houses. Each day, a postman goes to the post office, takes letters for the residents of one house, and delivers them. Then he returns to the post office, takes letters for the residents of another house, and delivers them again. He repeats this process for all the houses. Where should the post office be built so that the postman has to travel the shortest distance? The street can be considered a line segment.

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

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

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

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