
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 determinant operation defined as $\begin{vmatrix} x_1 & y_1 \\ x_2 & y_2 \end{vmatrix} = x_1 y_2 - x_2 y_1$, the function $f(x) = \begin{vmatrix} \sqrt{3} & \cos x \\ 1 & \sin x \end{vmatrix}$ is graphically shifted $\varphi (\varphi > 0)$ units to the right, resulting in an odd function. Determine the minimum value of $\varphi$.

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