
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
Xiao Mahu made a mistake in solving the inequality $\frac{1}{2}-\frac{x-2}{3} \gt 1$. The solution process is as follows:  
Multiply both sides of the inequality by $6$, we get $3-2\left(x-2\right) \gt 1$ (Step 1)  
Expand the brackets, we get $3-2x+4 \gt 1$ (Step 2)  
Rearrange terms and combine like terms, we get $-2x \gt -6$ (Step 3)  
Therefore, the solution is $x \lt 3$ (Step 4)  
$(1)$ Xiao Mahu made a mistake starting from step ______, and the reason for the mistake is ______.  
$(2)$ Please write down the correct solution process for this question.

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