
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 $\begin{vmatrix} a & b \\ c & d \end{vmatrix} =ad-bc$. If the complex number $x= \dfrac {1-i}{1+i}$, $y= \begin{vmatrix} 4i & 3-xi \\ 1+i & x+i \end{vmatrix}$, then $y=$ \_\_\_\_\_\_.

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