
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
There are  $n$  cities in a country, where  $n>1$ . There are railroads connecting some of the cities so that you can travel between any two cities through a series of railroads (railroads run in both direction.) In addition, in this country, it is impossible to travel from a city, through a series of distinct cities, and return back to the original city. We define the **degree** of a city as the number of cities directly connected to it by a single segment of railroad. For a city  $A$  that is directly connected to  $x$  cities, with  $y$  of those cities having a smaller degree than city  $A$ , the **significance** of city  $A$  is defined as  $\frac{y}{x}$ .

Find the smallest positive real number  $t$  so that, for any  $n>1$ , the sum of the significance of all cities is less than  $tn$ , no matter how the railroads are paved.

*Proposed by houkai*

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