
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
Solve the system of inequalities: $\left\{\begin{array}{l}{\frac{x-1}{2}＜2x+1①}\\{-3(1-x)≥-4②}\end{array}\right.$. Yuan Yuan's solution is as follows:  
Solution: From ①, we have $x-1 \lt 2x+1$, so $x \gt 2$.  
From ②, we have $1-x\geqslant 4$, so $x\leqslant 3$.  
Therefore, the solution set of the original system of inequalities is $2 \lt x\leqslant 3$.  
Is there any mistake in Yuan Yuan's solution? If there is, write down the correct solution process.

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