
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 highway running from west to east intersects with $n$ equivalent roads, numbered from 1 to $n$ consecutively. Cars travel on these roads from south to north and from north to south. The probability that a car approaches the highway from each road is $\frac{1}{n}$. Similarly, the probability that a car turns off the highway onto each road is $\frac{1}{n}$. The road that a car leaves the highway on does not depend on where the car entered the highway.

Find the probability that a random car, having entered the highway, will pass the $k$-th intersection (either driving through it or turning onto it).

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