
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
Given the function $f(x)=\sin x+ \sqrt {3}\cos x+2$, where $x\in[0,2\pi]$, and the equation $f(x)=m$ has two distinct real roots $\alpha$ and $\beta$, find the value of $\sin (\alpha+\beta)$.

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