
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
During the Yangmei season in Ningbo, local Cixi Yangmei is a taste of hometown in the hearts of Ningbo people. This year is a big year for Yangmei. In order to allow residents to taste high-quality and affordable Yangmei, a large-scale Yangmei planting household offers a discounted packaging method for 1000 kilograms of Yangmei. The packaging methods and prices are as follows: A round basket containing 8 kilograms is sold for 160 yuan per basket; a square basket containing 18 kilograms is sold for 270 yuan per basket. If these two packaging methods are used to pack all 1000 kilograms of Yangmei.<br/>$(1)$ If selling $a$ baskets of round baskets and $a$ baskets of square baskets brings in a total of 8600 yuan, find the value of $a$;<br/>$(2)$ When the total revenue from sales is 16760 yuan,<br/>① If this batch of Yangmei is all sold out, how many baskets of round baskets and square baskets were packed in total;<br/>② If the Yangmei planting household keeps $b\left(b \gt 0\right)$ baskets of round baskets to give away, and the rest of the Yangmei is all sold out, find the value of $b$.

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