
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 $f(x)$ is a function defined on $\mathbb{R}$, it has the following three properties:
1. The axis of symmetry of the graph of $f(x)$ is $x=2$.
2. On the interval $(-\infty, 0)$, $f(x)$ is monotonically increasing.
3. $f(x)$ has a maximum value of 4.

Please write a function $f(x)=$ that satisfies all the above three properties.

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