
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
Recently, Mr. Li just bought a small car. He recorded the distance the car traveled each day for 7 consecutive days (as shown in the table below). Using 50 kilometers as a standard, distances greater than 50 kilometers are recorded as "$+$", distances less than 50 kilometers are recorded as "$-$", and distances exactly 50 kilometers are recorded as "$0$".

|           | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Day 6 | Day 7 |
|-----------|-------|-------|-------|-------|-------|-------|-------|
| Distance (km) | $-8$ | $-11$ | $-14$ | $0$ | $-16$ | $+41$ | $+8$ |

$(1)$ Calculate the average distance traveled per day over these seven days.<br/>$(2)$ If it takes 6 liters of gasoline to travel 100 kilometers, and the price of gasoline is $7.7$ yuan per liter, calculate how much Mr. Li's family will spend on gasoline in a month (assuming 30 days).

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