
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 $y=4\sin (2x+ \frac {\pi}{6})$ where $x\in[0, \frac {7\pi}{6}]$, the graph intersects with the line $y=m$ at three points with the x-coordinates $x_{1}$, $x_{2}$, and $x_{3}$ ($x_{1} < x_{2} < x_{3}$). Find the value of $x_{1}+2x_{2}+x_{3}$.

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