
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 city is: a starting price of 5 yuan for the first 3 km (the minimum fare for taking a taxi once); after traveling 3 km, the fare is 1.2 yuan per kilometer; after traveling 10 km, an additional 50% empty fare is charged for each kilometer (i.e., the fare is 1.8 yuan per kilometer).

(1) Write the relationship between the fare and the distance traveled.
(2) A passenger has a journey of 30 km. To save money, he designed two taxi-riding plans:

a. Travel in two segments: take one taxi for 15 km, then switch to another taxi for the remaining 15 km.
b. Travel in three segments: take a taxi for 10 km, then switch to another taxi, and repeat this process once more.

Question: Which plan is more cost-effective?

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