
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
A parabola with the equation $y = ax^2 + bx + c$ is reflected about the x-axis and then both the original and its reflection are translated vertically, but in different directions by 3 units. If the new equations of the parabolas are $y=f(x)$ for the original and $y=g(x)$ for its reflection, what is the equation of $y = (f-g)(x)$?

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