
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
$(1)$ When Xiao Bo was studying algebraic expression evaluation, he found that for the algebraic expression $x\left(x-6\right)-\left(3-x\right)^{2}$, the calculated results were the same when different values were assigned to $x$. Please explain this phenomenon using the knowledge of simplifying algebraic expressions.<br/>$(2)$ The following is Xiao Ning's solution process for the inequality $x-2\left(x-3\right) \gt 1$:<br/>Solution: Removing the parentheses, we get: $x-2x-6 \gt 1$<br/>Rearranging terms, we get: $x-2x \gt 1+6$<br/>Combining like terms, we get: $-x \gt 7$<br/>Dividing both sides by $-1$, we get: $x \gt -7$<br/>Is there any mistake in Xiao Ning's solution process? If there is, please write out the correct solution process.

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