
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 the function \( f(x)=\frac{a}{a^{2}-2}\left(a^{x}-a^{-x}\right) \) (where \( a > 0 \) and \( a \neq 1 \)), which is an increasing function on the set of real numbers \(\mathbf{R}\), find the range of values for \(a\).

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