
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
Answer the following questions: (The teacher's explanation on the blackboard is as follows) Utilizing the laws of operations can sometimes simplify calculations. For example, $198\times 12=(100-2)\times 12=1200-24=1176$; For example, $-16\times 233+17\times 233=(-16+17)\times 233=233$  
$(1)$ Please refer to the teacher's explanation on the blackboard and simplify the calculations using the laws of operations (please provide the specific solution process):  
① $999\times (-13)$;  
② $999\times 118\frac{4}{5}+333\times (-\frac{3}{5})-999\times 18\frac{3}{5}$  
$(2)$ Calculate: $6\div (-\frac{1}{2}+\frac{1}{3})$.  
Fangfang's calculation process is as follows:  
Original expression $=6\div (-\frac{1}{2})+6÷\frac{1}{3}=-12+18=6$.  
Please determine if Fangfang's calculation process is correct. If not, please provide the correct calculation process.

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