
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
Given that the equation \( x^{2} + (m + 1)x - 2 = 0 \) has 2 integral roots \( (\alpha + 1) \) and \( (\beta + 1) \) with \( \alpha < \beta \) and \( m \neq 0 \). Let \( d = \beta - \alpha \).

G8.1 Find the value of \( m \).

G8.2 Find the value of \( d \).

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