
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 $y = ax^2 + bx + c$ ($a \neq 0$). The curve $C_1$ is symmetric to $C$ with respect to the $y$-axis, and the curve $C_2$ is symmetric to $C_1$ with respect to the $x$-axis. Then, the curve $C_2$ is the graph of the function $y = \boxed{\text{ }}$.

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