
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
According to the properties of equations and inequalities, we can compare the sizes of two quantities using the following method: if $A-B \gt 0$, then $A \gt B$; if $A-B=0$, then $A=B$; if $A-B \lt 0$, then $A \lt B$. This method of comparing sizes is called the "subtractive comparison method". Compare the sizes of $2x^{2}-2x+1$ and $x^{2}-2x$ using this method.

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