
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
Environmental issues have become a focal point of concern. To reduce the pollution of urban air by car exhaust, a city has decided to retrofit taxis to use liquefied gas instead of gasoline. The reason is that the combustion of liquefied gas does not produce harmful gases such as sulfur dioxide and nitrogen monoxide, which means it has little or no pollution to the atmosphere. Based on the following data:  
(1) The current price of gasoline is $2.8$ yuan per liter, and a taxi can travel about $12km$ per liter of gasoline;  
(2) The current price of liquefied gas is $3$ yuan per kilogram, and one kilogram of liquefied gas can travel an average of $15$ to $16km$;  
(3) A taxi travels an average distance of $200km$ per day.  
(a) From an economic perspective, evaluate which is more economical to use, liquefied gas or gasoline (i.e., which saves more money);  
(b) Assuming that retrofitting a taxi with liquefied gas equipment costs $5000$ yuan, how long will it take for the savings to equal the cost of retrofitting the equipment.

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