
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
Determine the number of points common to the graphs of
\[
(2x - 2y + 4)(6x + 2y - 8) = 0 \text{ and } (2x + 2y - 4)(4x - 10y + 14) = 0
\]
where the first equation in the second system is replaced by a parabola \(y = -x^2 + 2\).
A) 2
B) 4
C) 6
D) 8
E) Infinite

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