
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
Let the functions $f(x)$ and $g(x)$ be defined on $\mathbb{R}$ as an odd function and an even function, respectively, and satisfy $f(x)+g(x)=x^3-x^2+1$. Given that $f(x)$ is an odd function, find the value of $f(1)$.

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