
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 $f(x)=5\sin (2x-\theta)$, where $\theta\in(0, \frac{\pi}{2}]$ and $x\in[0,5\pi]$, if the function $F(x)=f(x)-3$ has all its zeros denoted sequentially as $x_{1}$, $x_{2}$, $x_{3}$, …, $x_{n}$, and $x_{1} < x_{2} < x_{3} < … < x_{n-1} < x_{n}$, with $n\in\mathbb{N}^*$, if $x_{1}+2x_{2}+2x_{3}+…+2x_{n-2}+2x_{n-1}+x_{n}= \frac{83}{2}\pi$, then $\theta=$ _______.

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