
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
Xinhua Stationery Store recently purchased a batch of pens at a cost of $6$ yuan each. In order to set a reasonable price, a flexible pricing strategy was implemented in the five days leading up to the sale. Each pen was priced at $10$ yuan, with any amount over $10$ yuan considered positive and any amount under $10$ yuan considered negative. The store recorded the selling price and quantity sold of these pens over the five days as shown in the table below:

|            | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 |
|------------|-------|-------|-------|-------|-------|
| Price Relative to Standard Price (yuan) | $+3$ | $+2$ | $+1$ | $-1$ | $-2$ |
| Quantity Sold (units) | $7$ | $12$ | $15$ | $32$ | $34$ |

$(1)$ The day with the highest profit over these five days is the ______ day, and the profit on that day is ______ yuan.  
$(2)$ How much money did Xinhua Stationery Store make from selling these pens over the five days?

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