
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 a function $f(x)$ is convex on the interval $D$, then for any $x\_1$, $x\_2$, $...$, $x\_n$ in the interval $D$, we have $\frac{f(x\_1) + f(x\_2) + ... + f(x\_n)}{n} \leqslant f(\frac{x\_1 + x\_2 + ... + x\_n}{n})$. If $y = \sin x$ is a convex function on the interval $(0, \pi)$, then the maximum value of $\sin A + \sin B + \sin C$ in $\triangle ABC$ is \_\_\_\_\_\_.

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