
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
Dan is walking down the left side of a street in New York City and must cross to the right side at one of 10 crosswalks he will pass. Each time he arrives at a crosswalk, he must wait \( t \) seconds, where \( t \) is selected uniformly at random from the real interval \([0, 60]\) ( \( t \) can be different at different crosswalks). Because the wait time is displayed on the signal across the street, Dan employs the following strategy: if the wait time when he arrives at the crosswalk is no more than \( k \) seconds, he crosses. Otherwise, he immediately moves on to the next crosswalk. If he arrives at the last crosswalk and has not crossed yet, then he crosses regardless of the wait time. Find the value of \( k \) which minimizes his expected wait time.

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