
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
The following is Xiaoying's process of solving a linear equation. Please read carefully and answer the questions.

解方程:$\frac{{2x+1}}{3}-\frac{{5x-1}}{6}=1$  
Solution:  
To eliminate the denominators, we get $2\left(2x+1\right)-\left(5x-1\right)=1$ ... Step 1  
Expanding the brackets, we get $4x+2-5x+1=1$ ... Step 2  
Rearranging terms, we get $4x-5x=1-1-2$ ... Step 3  
Combining like terms, we get $-x=-2$, ... Step 4  
Dividing both sides of the equation by $-1$, we get $x=2$ ... Step 5

$(1)$ The basis of the third step in the above solution process is ______.  
$A$. the basic property of equations  
$B$. the basic property of inequalities  
$C$. the basic property of fractions  
$D$. the distributive property of multiplication  
$(2)$ Errors start to appear from the ______ step;  
$(3)$ The correct solution to the equation is ______.

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