
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
Define any function on a symmetric interval about the origin as "the sum (or difference) of an odd function and an even function." Let $f(x)$ be any function defined on the domain $\mathbb{R}$, $$F(x)= \frac {f(x)+f(-x)}{2},$$ $$G(x)= \frac {f(x)-f(-x)}{2}.$$ Determine the parity of $F(x)$ and $G(x)$. Now, if the function $f(x)=\ln(e^x+1)$ is to be expressed as the sum of an odd function $g(x)$ and an even function $h(x)$, then $g(x)=$ ______.

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