
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
Below is Xiao Ying's process of solving the inequality $\frac{x+5}{2}-2＜\frac{3x+2}{2}$:<br/>① Clear the denominators, we get $x+5-2 \lt 3x+2$,<br/>② Rearrange terms and combine like terms, we get $-2x \lt -1$,<br/>③ Divide both sides by $-2$, we get $x＞\frac{1}{2}$.<br/>First read the above solving process, then answer the following questions.<br/>$(1)$ At which step did Xiao Ying make a mistake? Please write down the step number______;<br/>$(2)$ The reason for the mistake is______;<br/>$(3)$ The basis for step ③ is______;<br/>$(4)$ The solution set of the inequality should be______.

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