
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
The complex number w has positive imaginary part and satisﬁes  $|w| = 5$ . The triangle in the complex plane with vertices at  $w, w^2,$  and  $w^3$  has a right angle at  $w$ . Find the real part of  $w^3$ .


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