
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, especially in China, where the production and sales of new energy vehicles have increased significantly. Xiao Ming's family recently purchased a new energy pure electric vehicle. He recorded the daily distances traveled for 7 consecutive days (as shown in the table below). Using $50km$ as the 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 $(km)$ | $-8$ | $-12$ | $-16$ | $0$ | $+22$ | $+31$ | $+33$ |

$(1)$ Calculate the total distance traveled by Xiao Ming's new energy vehicle in these seven days.  
$(2)$ Given that a gasoline car consumes $5.5$ liters of gasoline per $100km$ at a price of $8.2$ yuan per liter, while a new energy vehicle consumes $15$ kWh per $100km$ at a cost of $0.56 yuan per kWh, estimate how much money Xiao Ming's family saved by switching to a new energy vehicle for these 7 days.

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