
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 is offering a discounted packaging method for 1000 kilograms of Yangmei. The packaging methods and prices are as follows: a round basket containing 8 kilograms, priced at 160 yuan per basket; a square basket containing 18 kilograms, priced at 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 all these Yangmei are sold out, please determine 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 are all sold out, please determine the possible packaging options for the household.

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