
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
A company plans to purchase two models of robots, $A$ and $B$, for material handling. It is known that robot $A$ can handle $30kg$ more material per hour than robot $B$, and the time it takes for robot $A$ to handle $1000kg$ of material is the same as the time it takes for robot $B$ to handle $800kg$ of material.  
$(1)$ Find out how much material each type of robot can handle per hour.  
$(2)$ The company plans to purchase a total of 20 robots of types $A$ and $B$, and requires that the robots handle at least $2800kg$ of material per hour. How many robots of type $A$ should be purchased at least?

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