
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
For the given natural numbers \(k_{0} < k_{1} < k_{2}\), determine the minimum number of roots in the interval \([0, 2\pi)\) that the equation

\[ \sin(k_{0} x) + A_{1} \cdot \sin(k_{1} x) + A_{2} \cdot \sin(k_{2} x) = 0 \]

can have, where \(A_{1}, A_{2}\) are real numbers.

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