
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 $f(x)=\sin(2ωx-\frac{π}{6})$, the graph is shifted to the left by $\frac{π}{4}$ units to obtain the graph of function $g(x)$. The graph of function $g(x)$ is symmetric about the $y$-axis. If $ω$ is the smallest positive number for which the transformation is valid, then $ω=$ \_\_\_\_\_\_.

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