
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 "Six Records of a Floating Life," it is said that "Buddha's hand is the gentleman among fragrances." Buddha's hand has a refreshing scent that soothes the heart and lungs when brewed in tea, making it very popular among people. In a certain place, Buddha's hand has been cultivated for over 600 years. A farmer harvested 8 Buddha's hand fruits, with each fruit weighing 0.5 kg as the standard. The excess weight is recorded as a positive number, and the deficient weight is recorded as a negative number. The records are as follows (unit: kg): 0.1, 0, -0.05, -0.25, 0.15, 0.2, 0.05, -0.1.
  
$(1)$ How many kilograms heavier is the heaviest Buddha's hand compared to the lightest one among the 8 harvested by the farmer?
  
$(2)$ Compared to the standard weight, how many kilograms do the total 8 Buddha's hand fruits exceed or fall short of?
  
$(3)$ If the selling price of Buddha's hand is $42 per kg, how much money can the farmer earn by selling these 8 Buddha's hand fruits?

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