
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
Let  $n>2$  be an integer. In a country there are  $n$  cities and every two of them are connected by a direct road. Each road is assigned an integer from the set  $\{1, 2,\ldots ,m\}$  (different roads may be assigned the same number). The *priority* of a city is the sum of the numbers assigned to roads which lead to it. Find the smallest  $m$  for which it is possible that all cities have a different priority.

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