
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
Uncle Xiao Wang's family is a professional pig farmer. The Tibetan fragrant pig and the local black pig they raise have always been popular among the citizens. Xiao Wang opened a pork store in October this year. It is known that the selling price of Tibetan fragrant pork is $30$ yuan per kilogram, and the selling price of local black pork is $20$ yuan per kilogram. Every day, a fixed amount of both types of pork, totaling $300$ kilograms, is purchased from Uncle's house and can be sold out completely.<br/>$(1)$ If the daily sales revenue is not less than $8000$ yuan, how many kilograms of Tibetan fragrant pork must be sold per day at least?<br/>$(2)$ Xiao Wang found that in October, he could sell all the pork in the morning every day, and the consumers highly praised the pork. Therefore, Xiao Wang decided to adjust the pork prices, increase the purchase amount, and be able to sell all the pork. He raised the price of Tibetan fragrant pork by $2a\%$, lowered the price of local black pork by $a\%$, compared to the sales volume when the minimum daily sales revenue was obtained in $(1)$, the sales volume of Tibetan fragrant pork decreased by $a\%$, and the sales volume of local black pork was twice the original. As a result, the daily sales revenue was $1750$ yuan more than the minimum daily sales revenue obtained in $(1)$. Find the value of $a$.

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