
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
In the northern region, there is a saying "three days after Mangzhong, you will see the wheat stubble." After "Mangzhong" each year is the busiest season for wheat harvesting. In a certain township in our county, the government introduced 20 harvesters, with 80 mu of wheat harvested per day by each type A harvester and 120 mu of wheat harvested per day by each type B harvester. All types of harvesters can harvest 2080 mu in one day.  
$(1)$ Find out how many type A and type B harvesters were introduced.  
$(2)$ Due to changes in weather conditions, in order to "store the grains" and "harvest and sow in time," the township needs to harvest more than 2900 mu of wheat in one day. To complete the task, they plan to introduce 8 more harvesters of these two types. How many different introduction plans are there? Please list them all.

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