
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 $f(x)=\sin 2x$, its graph intersects with the line $2kx-2y-kπ=0 (k > 0)$ at exactly three common points. The x-coordinates of these points in ascending order are $x_{1}$, $x_{2}$, $x_{3}$. Calculate the value of $(x_{1}-x_{3})\tan (x_{2}-2x_{3})$.

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