
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 the function $f(x)=\frac{2e^x}{e^x+1}$, determine which of the functions between $F(x)=f(x)+1$ and $G(x)=f(x)-1$ is an odd function. If $f(b)=\frac{3}{2}$, find the value of $f(-b)$.

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