
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 a certain area, $732$ tons of household waste need to be processed every day, requiring exactly $12$ type $A$ and $10$ type $B$ pre-treatment sites for processing. It is known that one type $A$ site can process $6$ tons more of household waste per day than one type $B$ site.  
$(1)$ Find out how many tons of household waste one type $B$ site can process per day.  
$(2)$ Due to the requirement of improving waste classification, each site will process $6$ tons less of household waste per day. If the area plans to add a total of $5$ type $A$ and type $B$ sites, how many additional type $A$ sites are needed at least to process the waste on the same day?

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