
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
Define the operation: $\begin{vmatrix} a_{1} & a_{2} \\ a_{3} & a_{4}\end{vmatrix} =a_{1}a_{4}-a_{2}a_{3}$, and consider the function $f(x)= \begin{vmatrix} \sqrt {3} & \sin \omega x \\ 1 & \cos \omega x\end{vmatrix} (\omega > 0)$. If the graph of $f(x)$ is shifted to the left by $\dfrac {2\pi}{3}$ units, and the resulting graph corresponds to an even function, then determine the minimum value of $\omega$.

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