
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 inequality system $\left\{\begin{array}{l}{1-\frac{2x-1}{2}>\frac{3x-1}{4}①}\\{2-3x\leq 4-x②}\end{array}\right.$.<br/>Below is a partial solution process from a student, please read carefully and complete the tasks:<br/>Solution: From ①, we have:<br/>$4-2\left(2x-1\right) > 3x-1\ldots $Step $1$<br/>$4-4x+2 > 3x-1\ldots $Step $2$<br/>$-4x-3x > -1-4-2$<br/>$-7x > -7\ldots $Step $3$<br/>$x > 1\ldots $Step $4$<br/>Task $1$: The student made a mistake in step $4$, the reason for the mistake is $x < 1$;<br/>The correct solution set for inequality ① is ______;<br/>Task $2$: Solve inequality ② and write down the solution set for this inequality system.

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