
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 recent years, the development of new energy vehicles has been rapid globally, and the production and sales of new energy vehicles in China have increased significantly. Xiao Wang's family has recently replaced their old car with a new pure electric new energy vehicle. He recorded the daily distances traveled for 7 consecutive days as shown in the table below. Using $50km$ as a standard, distances greater than $50km$ are recorded as "$+$", distances less than $50km$ are recorded as "$-$", and distances exactly $50km$ are recorded as "$0$".

|           | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
|-----------|-------|-------|-------|-------|-------|-------|-------|
| Distance (km) | $-8$ | $-12$ | $-16$ | $0$ | $+22$ | $+31$ | $+33$ |

$(1)$ The day with the longest distance traveled in these 7 days compared to the day with the shortest distance traveled is ______ $km$ more.  
$(2)$ How many kilometers did Xiao Wang's new energy vehicle travel in total over these seven days?  
$(3)$ It is known that a gasoline car consumes $5.5$ liters of gasoline for every $100km traveled, with gasoline priced at $8.4$ yuan per liter. On the other hand, a new energy vehicle consumes $15$ kWh of electricity for every $100km traveled, with each kWh costing $0.5$ yuan. How much money did Xiao Wang's family save in travel expenses over these 7 days after switching to the new energy vehicle?

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