
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. On these roads, cars travel from south to north and from north to south. The probability that a car approaches the highway via each of these roads is \( \frac{1}{n} \). Similarly, the probability that a car turns off the highway onto each of these roads is \( \frac{1}{n} \). The road through which a car exits the highway does not depend on where it entered the highway. Find the probability that a random car entering the highway will bypass the \( k \)-th intersection (either by passing it straight or by turning onto it).

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