
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
\[z = \frac{(-7 + 8i)^5 \cdot (17 - 9i)^3}{2 + 5i},\] and let \(w = \frac{\overline{z}}{z}\). Compute \(|w|\).

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