
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 $|\begin{matrix}a & c \\ b & d\end{matrix}| = ad - bc$, and the complex number $Z$ satisfies $|\begin{matrix}z & i \\ 1 & i\end{matrix}| = 1 + i$, find the modulus of $Z$ (denoted as $|Z|$).

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