
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
To speed up the efficiency of product production, a factory will use two types of machines, $A$ and $B$, to produce products. It is known that machine $A$ produces $10kg$ more per hour than machine $B$, and the time it takes for machine $A$ to produce $600kg$ of products is equal to the time it takes for machine $B$ to produce $500kg$ of products.  
$(1)$ Find out how many $kg$ of products each machine produces per hour.  
$(2)$ In order to complete a task of producing at least $1000kg$ of products within an hour, the factory decides to use a total of $18$ machines of types $A$ and $B$ simultaneously. How many machines of type $A$ are needed at least?

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