
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 the function \( f(x) = ax^2 + bx + c \) where \( a \neq 0 \) and \( a, b, c \) are constants, the function \( f_1(x) \) is the reflection of the function \( f(x) \) about the y-axis. The function \( f_2(x) \) is the reflection of the function \( f_1(x) \) about the line \( y = 1 \). Determine the explicit form of the function \( f_2(x) \).

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