
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
Properties of convex polygons: If the function $f(x)$ is convex on the interval $D$, then for any $n$ variables $x_1, x_2, \ldots, x_n$ within the interval $D$, it holds that $$\frac{f(x_{1})+f(x_{2})+\ldots+f(x_{n})}{n} \leq f\left( \frac{x_{1}+x_{2}+\ldots+x_{n}}{n}\right),$$ and the equality holds if and only if $x_1=x_2=\ldots=x_n$. Given that the function $y=\sin x$ is convex,  
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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