
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 city can be divided into a rectangular shape consisting of several blocks: it has $n$ streets parallel to each other, and another set of $m$ streets intersects the first group at right angles. Some policemen are on duty on the streets (but not at intersections). Each policeman reports the bus numbers, running directions, and the time when the buses passed by. In order to reconstruct the route of a bus traveling along a loop (without repeating any segment of the streets) based on the information provided by the policemen, what is the minimum number of policemen needed to be on duty on the streets?

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