
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
The notation $[x]$ represents the greatest integer less than or equal to $x$ (for example, $[\sqrt{5}] = 2$). Let $n$ be a natural number, and let $I = (n+1)^2 + n - [\sqrt{(n+1)^2 + n + 1}]^2. $ Determine the possible values of the expression $I$.

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