
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 $n$ in order. Cars travel on these roads from south to north and from north to south. The probability that a car will approach the highway from each road is $\frac{1}{n}$. Similarly, the probability that a car will turn off the highway onto each road is also $\frac{1}{n}$. The road by which a car leaves the highway does not depend on where the car entered the highway.

Find the probability that a random car that entered the highway will pass through the $k$-th intersection (either going straight through or turning at it).

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