
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 \( f(x) = x^4 - 4x^3 + (3 + m)x^2 - 12x + 12 \), where \( m \) is a real number.

1. Find all integer \( m \) such that the equation \( f(x) - f(1 - x) + 4x^3 = 0 \) has at least one integer solution.
2. Find all values of \( m \) such that \( f(x) \geqslant 0 \) for every real number \( x \).

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