
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
Let \( z \in \mathbf{C} \) satisfy the equation \( a z^{n} + b \mathrm{i} z^{n-1} + b \mathrm{i} z - a = 0 \), where \( a, b \in \mathbf{R} \) and \( n \in \mathbf{N} \). Find \( |z| \).

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