
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 $a \in \mathbb{R}$ and $b \in [0, 2\pi]$, for any real number $x$, $\sin\left(3x - \frac{\pi}{3}\right) = \sin\left(ax + b\right)$. Determine the number of ordered real number pairs $(a, b)$ that satisfy the given condition.

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