
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 \[ f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 \] and \[ g(x) = 3 - 2x - 6x^3 + 8x^4 + x^5. \] Find $c$ such that the polynomial $f(x) + cg(x)$ has degree 4.

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