
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 the functions $f(x) = 3\sin\left(ωx - \frac{π}{6}\right) (ω > 0)$ and $g(x) = 3\cos(2x + φ)$ have identical symmetric centers in their graphs, and $x ∈ \left[0, \frac{π}{2}\right]$, determine the range of values for $f(x)$.

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