
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
To obtain the graph of the function $y=\sin \left(2x-\frac{\pi }{3}\right)$, we only need to transform the graph of the function $y=\sin x$ as follows:

(1) First, shrink each $x$ value to its original $\frac{1}{2}$ times, keeping $y$ value unchanged, and then shift it to the right by $\frac{\pi }{6}$ units.

(2) First, shift to the right by $\frac{\pi }{3}$ units, and then shrink each $x$ value to its original $\frac{1}{2}$ times, keeping $y$ value unchanged.

(3) First, shift to the right by $\frac{\pi }{6}$ units, and then shrink each $x$ value to its original $\frac{1}{2}$ times, keeping $y$ value unchanged.

(4) First, shrink each $x$ value to its original $\frac{1}{2}$ times, keeping $y$ value unchanged, and then shift it to the left by $\frac{5\pi }{6}$ units.

Find all the correct options.

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