
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 - $\frac{π}{3}$), if the solutions to the equation f(x) = $\frac{1}{3}$ in the interval (0, π) are x₁ and x₂ (x₁ < x₂), find the value of sin(x₁ - x₂).

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