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

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