
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 the function $f(x)$ is convex on the interval $D$, then for any $x_{1}$, $x_{2}$, $\ldots$, $x_{n}$ 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 convex on the interval $(0,\pi)$, then in $\triangle ABC$, the maximum value of $\sin A+\sin B+\sin C$ is ____.

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