
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 function $f(x)$ whose graph passes through the point $(4,3)$. The length of the segment it cuts on the $x$-axis is $2$, and for any $x \in \mathbb{R}$, it holds that $f(2-x) = f(2+x)$. Find the expression for $f(x)$.

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