
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 $f(x)=4\sin(2x+\frac{\pi}{6})$, where $(0 \leqslant x \leqslant \frac{91\pi}{6})$, if the function $F(x)=f(x)-3$ has all its zeros denoted sequentially as $x_1$, $x_2$, $x_3$, ..., $x_n$, and $x_1 < x_2 < x_3 < ... < x_n$, then the value of $x_1+2x_2+2x_3+…+2x_{n-1}+x_n=$ __________.

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