
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 is laid out as a rectangle, divided into cells: $n$ streets are parallel to each other, and $m$ other streets intersect them at right angles. Policemen stand on the streets of the city, but not at intersections. Each policeman reports the number of the passing car, its direction of travel, and the time it passed. What is the minimum number of policemen needed to uniquely determine the path of any car traveling on a closed route (the route does not pass the same street segment twice)?

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