
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 operation defined as $\begin{vmatrix} \begin{matrix}a & b \\ c & d\end{matrix} \end{vmatrix} =ad-bc$, let $x=\frac{2-i}{3+i}$, and $y=\begin{vmatrix} \begin{matrix}4i & 3-xi \\ 1+i & x+i\end{matrix} \end{vmatrix}$, find the value of $y$.

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