
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
In a certain city, the initial fare for taxis is 10 yuan. If the travel distance does not exceed 4km, the fare is charged at a standard rate of 10 yuan. If the travel distance exceeds 4km, an additional 2 yuan is charged for each kilometer exceeded (fractions of a kilometer are rounded up to the nearest kilometer). The distance from the city's civil aviation airport to a certain hotel is 15km. A driver frequently shuttles passengers between the airport and this hotel. Due to different driving routes and the need to convert stopping time into driving distance (the city stipulates that every 5 minutes of stopping time is equivalent to 1km of driving distance), the driving distance $\xi$ for this driver when shuttling passengers is a random variable, and the fare charged to passengers $\eta$ is also a random variable.

(1) Find the relationship between the fare $\eta$ and the driving distance $\xi$.

(2) Given that a passenger actually paid a fare of 38 yuan, and the taxi actually traveled 15km, how many minutes at most did the taxi stop on the way due to various reasons?

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