
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 $\omega$ and $t > 0$, the function $$f(x)= \begin{vmatrix} \left.\begin{matrix}\sqrt {3} & \sin\omega x \\ 1 & \cos\omega x\end{matrix}\right.\end{vmatrix}$$ has a minimum positive period of $2\pi$. If the graph of $f(x)$ is shifted to the left by $t$ units, and the resulting graph corresponds to an even function, then the minimum value of $t$ is \_\_\_\_\_\_.

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