
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
Since we started using letters to represent numbers, we have found that expressing numbers and quantity relationships with algebraic expressions is more concise and clear, which helps us discover more interesting conclusions. Please try as required.<br/>$(1)$ Express with algebraic expressions:<br/>① The square of the difference between $a$ and $b$;<br/>② The difference between the sum of the squares of $a$ and $b$ and twice the product of $a$ and $b$;<br/>$(2)$ When $a=3$ and $b=-2$, find the values of the algebraic expressions listed in question (1) ① and ②;<br/>$(3)$ Based on the results of question (2), what equation did you discover?<br/>$(4)$ Using the conclusion you discovered: find the value of $2021^{2}-2021\times 4034+2017^{2}$.

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