
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
【Information Extraction】  
In some cases, it is not necessary to calculate the result to remove the absolute value symbol. For example: $|6+7|=6+7$, $|6-7|=7-6$, $|7-6|=7-6$, $|-6-7|=6+7$.  
【Initial Experience】  
$(1)$ According to the above rules, write the following expressions in the form without absolute value symbols (do not calculate the result):  
① $|7-21|=$______;  
② $|{-\frac{1}{2}+\frac{4}{5}}|=$______;  
③ $|{\frac{7}{{17}}-\frac{7}{{18}}}|=\_\_\_\_\_\_.$  
【Extended Application】  
$(2)$ Calculate:  
④ $|{\frac{1}{5}-\frac{{150}}{{557}}}|+|{\frac{{150}}{{557}}-\frac{1}{2}}|-|{-\frac{1}{2}}|$;  
⑤ $|{\frac{1}{3}-\frac{1}{2}}|+|{\frac{1}{4}-\frac{1}{3}}|+|{\frac{1}{5}-\frac{1}{4}}|+…+|{\frac{1}{{2021}}-\frac{1}{{2020}}}|+|{\frac{1}{{2022}}-\frac{1}{{2021}}}|$.

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