
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 exponential function, and $f(1 + \sqrt {3}) \cdot f(1 - \sqrt{3}) = 9$, if $g(x)$ is the inverse function of $f(x)$, then find the value of $g(\sqrt{10} + 1) + g(\sqrt{10} - 1)$.

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