
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 points $A(x\_1, x\_1^2)$ and $B(x\_2, x\_2^2)$ on the graph of the function $y = x^2$, it is known that segment $AB$ is always located above the function's graph between points $A$ and $B$. Therefore, the conclusion $\frac{x\_1^2 + x\_2^2}{2} > (\frac{x\_1 + x\_2}{2})^2$ holds true. By applying analogous thinking, if points $A(x\_1, \sin x\_1)$ and $B(x\_2, \sin x\_2)$ are on the graph of the function $y = \sin x (x \in (0, \pi))$, then a similar conclusion _______ holds true.

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