
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 $f(x)$ and $g(x)$ are odd and even functions defined on $\mathbb{R}$ respectively, and $f(x)-g(x)=(\frac{1}{2})^{x}$, determine the relationship among $f(-1)$, $f(0)$, and $g(1)$ in ascending order.

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