
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
A stationery store purchased a batch of pens at a cost of $6$ yuan each, with a total of 160 pens. In order to set a reasonable price, a flexible pricing strategy was implemented for the first four days before regular pricing. The selling price for each pen was set at $10$ yuan, with any price above $10$ yuan recorded as positive and any price below $10$ yuan recorded as negative. The store recorded the selling prices and sales quantities of the pens for these five days as shown in the table below:

|            | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 |
|------------|-------|-------|-------|-------|-------|
| Price Relative to Standard Price (yuan) | $+2$ | $+1$ | $0$ | $+1$ | $-2$ |
| Number of Pens Sold | 9 | 12 | 20 | 26 | 42 |

$(1)$ Among these five days, the highest selling price was on the ______ day, and the price on that day was ______ yuan.<br/>$(2)$ On which day did the store make the most profit during these five days? How much profit was made?<br/>$(3)$ During a store celebration, the pens were sold at a 10% discount off the base price of $10$ yuan, and all remaining pens were sold that day. How much profit did the store make on that day?

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