
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) = sinx, whose graph intersects with the line kx - y - kπ = 0 (k > 0) at exactly three points. The x-coordinates of these points, in ascending order, are x₁, x₂, and x₃. Calculate the value of $$\frac{tan(x_{2} - x_{3})}{x_{1} - x_{2}}$$.

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