
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 $f(x)$ be a function with the domain of $R$. It is known that $f(x)$ is an even function, and $f(x+1)$ is an odd function. When $x\in [1,2]$, $f(x)=\frac{a}{x}+b$. If $f(0)+f(1)=-4$, then $f(-\frac{1}{2})=\_\_\_\_\_\_$.

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