
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
Xibaipo is a national $5A$-level tourist scenic spot located in Shijiazhuang City, Hebei Province, China. It is one of the famous revolutionary memorial sites in China, now with attractions such as the Xibaipo Memorial Hall and the Xibaipo Stone Carving Park. A certain type of souvenir in the scenic area has a cost price of $5$ yuan per piece and is sold at a price of $8$ yuan per piece. It can sell 100 pieces per day. For every decrease of $0.1$ yuan in the selling price, an additional 10 pieces can be sold per day. Let the selling price of the souvenir decrease by $x$ yuan.<br/>$(1)$ When the selling price of each souvenir is $7$ yuan, the daily sales volume is ______ pieces.<br/>$(2)$ If the daily profit is $375$ yuan, in order to reduce the inventory quickly, what should be the selling price per piece?

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