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

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