
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
Consider a function $f(x)$ defined on the set of real numbers, $\mathbb{R}$, with the property that $y=f(x+1)$ is an even function. Additionally, for $x \geq 1$, the function is defined as $f(x) = \left(\frac{1}{2}\right)^x - 1$. Determine the relationships among $f\left(\frac{2}{3}\right)$, $f\left(\frac{3}{2}\right)$, and $f\left(\frac{1}{3}\right)$.

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