
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
Read and think:<br/>Given the following five equations:<br/>$3^{2}-1^{2}=8=8\times 1$<br/>$5^{2}-3^{2}=16=8\times 2$<br/>$7^{2}-5^{2}=24=8\times 3$<br/>$9^{2}-7^{2}=32=8\times 4$<br/>$11^{2}-9^{2}=40=8\times 5$<br/>By observation, we can conclude that the difference of the squares of two consecutive odd numbers must be divisible by $8$.<br/>The proof process is as follows:<br/>Let: the two consecutive odd numbers are $2n-1$ and $2n+1$ (where $n$ is an integer).<br/>Then $\left(2n+1\right)^{2}-\left(2n-1\right)^{2}$<br/>$=(4n^{2}+4n+1)-(4n^{2}-4n+1)$<br/>$=4n^{2}+4n+1-4n^{2}+4n-1$<br/>$=8n$<br/>Since $n$ is an integer, $8n$ must be divisible by $8$.<br/>Therefore, the difference of the squares of two consecutive odd numbers must be divisible by $8$.

Task 1: The "basis" in the material refers to the multiplication formula.

Task 2: In fact, the difference of the squares of any two odd numbers must also be a multiple of $8$. Please provide a proof (Hint: Let the two odd numbers be $2m+1$ and $2n+1$ where $m$ and $n$ are integers, and $m\neq n$).

Task 3: Is the difference of the squares of any two consecutive even numbers also a multiple of $8$? If yes, please provide a proof; if not, write down the conclusion you think is correct.

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