
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 a parabola with the vertex form $y = a(x-h)^2 + k$. This parabola is reflected about the x-axis and then each of the parabolas and its reflection are translated horizontally by 7 units in opposite directions. Find the equation of the graph of $y = (f + g)(x)$.

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