
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
If the function \( f(x) = \log_{a}\left(x + \sqrt{b x^{2} + 2 a^{2}}\right) \) (where \( a > 0 \) and \( a \neq -1 \)) is an odd function, then the pair of real numbers \((a, b) = \qquad\) .

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