
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 two distinct points $A(x\_1, \log x\_1)$ and $B(x\_2, \log x\_2)$ on the graph of the function $f(x) = \log x$, it is known that the line segment $AB$ is always located below the function graph between points $A$ and $B$. Therefore, the conclusion $\frac{\log x\_1 + \log x\_2}{2} < \log(\frac{x\_1 + x\_2}{2})$ holds. By applying analogous thinking, if points $A(x\_1, 2^{x\_1})$ and $B(x\_2, 2^{x\_2})$ are on the graph of the function $g(x) = 2^x$, then a similar conclusion can be drawn.

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