
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 an odd function $f(x)$ and an even function $g(x)$ defined on $\mathbb{R}$, satisfying $f(x)+g(x)=a^{x}-a^{-x}+2$ ($a > 0$, and $a \neq 1$), find the value of $f(2)$.

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