
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 $f(x)$ defined on the interval $D$ satisfies $\frac{1}{n}[f(x_{1})+f(x_{2})+\ldots+f(x_{n})] \leqslant f\left( \frac{x_{1}+x_{2}+\ldots+x_{n}}{n} \right)$ for $n$ values $x_{1}$, $x_{2}$, $\ldots$, $x_{n}$ in $D$, the function $f(x)$ is called a convex function on $D$. It is known that $f(x)=\sin x$ is a convex function on $(0,\pi)$. 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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