
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
\[ z = \frac{(3 - 4i)^2 \cdot (10 + 6i)^3}{5 + 12i}, \]
and let $w = (1 + 2i) \frac{\overline{z}}{z}.$ Compute $|w|$.

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