
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
It is found that the sum of the squares of any five consecutive integers is a multiple of $5$. Verify how many times the result of $\left(1\right)\left(-1\right)^{2}+0^{2}+1^{2}+2^{2}+3^{2}$ is a multiple of $5$. $(2)$ Given that one of the five consecutive integers is $n$, write down the sum of their squares and explain why it is a multiple of $5$.

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