
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
Below is Xiao Ming's process of solving the quadratic equation $2x\left(x-5\right)=3\left(5-x\right)$:<br/>Solution: The original equation can be simplified to $2x\left(x-5\right)=-3\left(x-5\right)$, $\ldots \ldots $ Step 1<br/>Dividing both sides of the equation by $\left(x-5\right)$, we get $2x=-3$, $\ldots \ldots $ Step 2<br/>By adjusting the coefficients to $1$, we get $x=-\frac{3}{2}$. Is Xiao Ming's solution correct? If correct, please explain the reason; if incorrect, please point out the step where the error occurred, analyze the reason for the error, and provide the correct solution process.

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