
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
Consider the polynomials \( f(x) = 3 + 8x - 4x^2 + 6x^3 - 7x^4 \) and \( g(x) = 5 - 3x + x^2 - 8x^3 + 11x^4 \). Find \( c \) such that the polynomial \( f(x) + c g(x) \) has degree 3.

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