
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 \[f(x)=2 - 15x + 4x^2 - 5x^3 + 6x^4\] and \[g(x)=5 - 3x - 7x^3 + 10x^4.\]
Find $c$ such that the polynomial $f(x) + cg(x)$ has degree 3.

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