
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
On the same set of axes are drawn the graph of $y=a(x-h)^2 + d$ and the graph obtained by replacing $x$ with $x+3$ in the given equation. If these two graphs intersect, where do they do so?
1. $y = a(x-h)^2 + d$
2. $y = a((x+3)-h)^2 + d$
A) At point $(\frac{3}{2}, a\left(\frac{3}{2}-h\right)^2 + d)$
B) At point $(-\frac{3}{2}, a\left(-\frac{3}{2}-h\right)^2 + d)$
C) At no points
D) At two points on the x-axis
E) At the origin

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