
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
Let the curve \( C \) be the graph of the function \( y = ax^2 + bx + c \) where \( a \neq 0 \). The curve \( C \) is reflected about the y-axis to get the curve \( C_1 \), and then \( C_1 \) is reflected about the x-axis to get the curve \( C_2 \). What is the equation of the curve \( C_2 \)?

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