
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 an even function defined on $\mathbb{R}$ and satisfies $f(x+2)=-\frac{1}{f(x)}$. If $f(x)=x$ for $2\leq x \leq 3$, find the value of $f\left(-\frac{11}{2}\right)$.

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