
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
The theorem of the property of convex functions states that if a function $f(x)$ is convex in the interval $D$, then for any $x\_1$, $x\_2$, $…$, $x\_n$ in the interval $D$, $\frac{f(x\_1)+f(x\_2)+…+f(x\_n)}{n} \leqslant f(\frac{x\_1+x\_2+…x\_n}{n})$. Given that the function $y=\sin x$ is convex in the interval $(0,\pi)$, find the maximum value of $\sin A + \sin B + \sin C$ in $\triangle ABC$.

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