
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 $n$. Cars are traveling on these roads from the south to the north and from the north to the south. The probability that a car approaches the highway from each of the roads is $\frac{1}{n}$. Similarly, the probability that a car turns off the highway onto each of the roads is $\frac{1}{n}$. The road that a car uses to leave the highway is independent of the point 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 passing straight through or turning at that intersection).

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