
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 wheat harvest season, to ensure that the wheat grains are stored in the granary, a farm arranges for two types of harvesters, $A$ and $B$, to harvest wheat. It is known that one $A$ harvester harvests $2$ hectares more wheat on average per day than one $B$ harvester. A $A$ harvester takes the same amount of time to harvest $15$ hectares of wheat as a $B$ harvester takes to harvest $9$ hectares of wheat.<br/>$(1)$ How many hectares of wheat does one $A$ harvester and one $B$ harvester harvest on average each day?<br/>$(2)$ The farm arranges for a total of $12$ harvesters of both types to harvest wheat simultaneously. To ensure that at least $50$ hectares of wheat are harvested each day, how many $A$ harvesters should be arranged at least?

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