
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
Given a quadratic equation $y = ax^2 + bx + c$ and its symmetric about the y-axis $y = a(x-h)^2 + b(x-h) + c$ with $h \neq 0$. If $b \neq 0$, $a \neq 0$, and the constant term in the symmetric equation is different, where $d \neq c$, these two graphs will intersect:
A) $\left(0, \frac{a(d-c)^2}{b^2} + d\right)$  
B) $\left( \frac{d-c}{b}, \frac{a(d-c)^2}{b^2} + d \right)$  
C) $\left(h, \frac{a(d-c)^2}{b^2} + d\right)$  
D) None of the above

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