
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 clothing store purchased a batch of thermal underwear at a cost of $50$ yuan per set. In order to set a reasonable price, a price adjustment sales event was held for $5$ days. The selling price was set at $70$ yuan per set, with any excess amount considered positive and any shortfall considered negative, as shown in the table below:

|            | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 |
|------------|-------|-------|-------|-------|-------|
| Price Relative to Standard Price (yuan) | $+5$ | $+2$ | $+1$ | $0$ | $-2$ |
| Number of Sets Sold | $7$ | $10$ | $15$ | $20$ | $23$ |

$(1)$ By how much did the total amount earned by selling this batch of thermal underwear in the store over these $5$ days exceed or fall short of the standard price?<br/>$(2)$ Calculate the total profit made by the store from selling this batch of thermal underwear over these $5$ days. (Profit $=$ Selling Price $-$ Cost Price)

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