
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 $\mathbb{R}$ that satisfy $f(x) + g(x) = a^x - a^{-x} + 2$ (where $a > 0$ and $a \neq 1$), if $g(2) = a$, then find the value of $f(2)$.

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