
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 process of solving the equation $3\left(2x-5\right)=\left(2x-5\right)^{2}$ by two students, Xiao Ming and Xiao Liang, is shown in the following table:<br/><table class="edittable"><tbody><tr><td width="275">Xiao Ming:<br/>Divide both sides by $\left(2x-5\right)$, we get<br/>$3=2x-5$.<br/>Therefore, $x=4$.</td><td width="275">Xiao Liang:<br/>Rearrange the equation, we get $3\left(2x-5\right)-\left(2x-5\right)^{2}=0$. Factor out the common factor, we get $\left(2x-5\right)\left(3-2x-5\right)=0$.<br/>Therefore, $2x-5=0$ or $3-2x-5=0$<br/>Solving gives $x_{1}=\frac{5}{2}$, $x_{2}=-1$.</td></tr></tbody></table>Task 1: Do you think their solutions are correct? If correct, mark with "$\surd $"; if incorrect, mark with "$\times $";<br/>Xiao Ming______, Xiao Liang______;<br/>Task 2: Write down your solution process.

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