
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
Person A and person B work on two production lines, $A$ and $B$, respectively, to process parts. On production line $A$, both person A and person B can process at least $2$ type $A$ parts per day. When continuously working, person A can process $10$ type $A$ parts on the first day, and the number of parts processed decreases by $2$ each consecutive day. Person B can process $8$ type $A$ parts on the first day, and the number of parts processed decreases by $1$ each consecutive day. On production line $B$, person A processes $7$ type $B$ parts per day, and person B processes $8$ type $B$ parts per day. They cannot work on the same production line on the same day, and they can change production lines after working continuously for at least $3$ days. According to the question:<br/>$(1)$ The maximum number of type $A$ parts that person A can process continuously on production line $A$ for $3$ days is ______ parts;<br/>$(2)$ If one type $A$ part and one type $B$ part make up a set of products, then the maximum number of sets of products that can be processed in $14$ days is ______ sets.

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