
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 $a, b \in \mathbb{R}$ and $c \in [0, 2\pi)$, if $2\sin\left(3x - \frac{\pi}{3}\right) = a\sin(bx + c)$ holds for any real number $x$, find the number of ordered triplets of real numbers $(a, b, c)$ that satisfy the condition.

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