
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 that $f(x)$ is a function defined on the real numbers $\mathbb{R}$, and it satisfies $f(x)f(x+2)=-1$. When $1 < x < 2$, $f(x) = x^3 + \sin\left(\frac{\pi}{9}x\right)$. Evaluate the value of $f(5.5)$.

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