
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 $f(x)=2\sin (2x+ \frac {π}{6})+a-1 (a\in R)$ has two distinct zeros $x\_1$, $x\_2$ in the interval $[0, \frac {π}{2}]$, find the range of $x\_1+x\_2+\sin (2x\_1+ \frac {π}{6})+\sin (2x\_2+ \frac {π}{6})$.

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