
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
A function $f(x)$ is defined on the set of real numbers $\mathbb{R}$ and is odd. It satisfies the condition $f(x) = -f(x + 2)$, and is decreasing on the interval $[1, 2]$. Determine the correct ordering of the function values at the points $\frac{1}{2}$, $-\frac{3}{2}$, and $3$.

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