
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
Technology changes the world. Express sorting robots have become popular from Weibo to Moments. According to the introduction, these robots can not only automatically plan the optimal route, accurately place packages in the corresponding compartments, sense and avoid obstacles, automatically return to the team to pick up packages, but also find charging piles to charge themselves when they run out of battery. A certain sorting warehouse plans to sort an average of 200,000 packages per day. However, the actual daily sorting volume may deviate from the plan. The table below shows the situation of sorting packages in the third week of October in this warehouse (the part exceeding the planned amount is recorded as positive, and the part that does not reach the planned amount is recorded as negative):

| Day of the Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
|-----------------|--------|---------|-----------|----------|--------|----------|--------|
| Sorting Situation (in 10,000s) | +6 | +4 | -6 | +8 | -1 | +7 | -4 |

$(1)$ The day with the most sorted packages in the warehouse this week is ______; the day with the least sorted packages is ______; the day with the most sorted packages has ______ more packages than the day with the least sorted packages;<br/>$(2)$ How many packages, on average, did the warehouse actually sort per day this week?

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