
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 that $0 < x_1 < x_2 < π$, and $\sin(2x_1 - \frac{π}{3}) = \sin(2x_2 - \frac{π}{3}) = \frac{4}{5}$, find the value of $\cos(x_1 - x_2)$:

A) $\frac{4}{5}$
B) $\frac{4}{5} \text{ or } -\frac{4}{5}$
C) $\frac{3}{5} \text{ or } -\frac{3}{5}$
D) $\frac{3}{5}$

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