
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 function $f(x)$ defined on $\mathbb{R}$ such that $f(1+x) + f(1-x) = 0$, and $f(x-1)$ is symmetric about $x=1$. When $x \in [0,2]$, $f(x) = ax^{2} + b$. If $f(0) + f(3) = 2$, then $f(\frac{7}{2}) = \_\_\_\_\_\_$.

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