
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 for any $n$ values $x_1$, $x_2$, ..., $x_n$ in $D$ the condition $\frac{1}{n}\left[ f(x_1) + f(x_2) + \cdots + f(x_n) \right] \leqslant f\left( \frac{x_1 + x_2 + \cdots + x_n}{n} \right)$,

then $f(x)$ is called a convex function on $D$. It is known that the function $y = \sin x$ is a "convex function" 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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