
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
Let the polynomial \( p(x) = a x^{3} + b x^{2} + c x + d \), where \( a, b, c, d \) are constants. If \( p(x) \) is divided by \( x^{2} + x + 2 \), the remainder is \( x + 2 \), and if \( p(x) \) is divided by \( x^{2} + x - 2 \), the remainder is \( 3x + 4 \). Find \( a, b, c, d \).

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