
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 \( f(x) = x^4 + ax^3 + bx^2 + cx + d \) be a polynomial where \( a, b, c, d \) are constants and \( x^4 \) represents the highest power with \( a < b < c < d \). Let \( g(x) \) be another polynomial whose roots are \( 2 \) times the roots of \( f(x) \). What is \( g(1) \) in terms of \( a, b, c, \) and \( d \)?
A) \( -8(16 + 8a + 4b + 2c + d) \)
B) \( 16 + 8a + 4b + 2c + d \)
C) \( -126 - 17a - 9b - 5c - 2d \)
D) \( 128 + 64a + 32b + 16c + 8d \)

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