
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
If the determinant operation is defined as $ \begin{vmatrix} a_1 & a_2 \\ a_3 & a_4 \end{vmatrix} =a_1a_4-a_2a_3 $, and the function $ f(x)= \begin{vmatrix} \sqrt{3} & \sin x \\ 1 & \cos x \end{vmatrix} $ is shifted to the left by $n$ units, determine the smallest possible value of $n$ for which the resulting graph is symmetric about the y-axis.

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