
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 \( f(x) = 2 - 5x + 4x^2 - 3x^3 + 7x^5 \) and \( g(x) = 1 - 7x + 5x^2 - 2x^4 + 9x^5 \). Find \( c \) such that the polynomial \( f(x) + c g(x) \) has degree 4.

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