
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
The taxi fare standard in a certain county town is: The starting price is 5 yuan (if the ride does not exceed 3 kilometers); after traveling 3 kilometers, the fare per kilometer is 1.2 yuan; after traveling 10 kilometers, the fare per kilometer is 1.8 yuan.  
(1) Write the relationship between the fare and the distance;  
(2) A customer plans a journey of 30 kilometers and, to save money, he designs three travel plans:  
① Do not change taxis: Take one taxi for 30 kilometers;  
② Take taxis in two segments: First, take one taxi for 15 kilometers, then change to another taxi for another 15 kilometers;  
③ Take taxis in three segments: Change taxis every 10 kilometers.  
Which plan is the most cost-effective?

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