
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
Determine the range of  $w(w + x)(w + y)(w + z)$ , where  $x, y, z$ , and  $w$  are real numbers such that
\[x + y + z + w = x^7 + y^7 + z^7 + w^7 = 0.\]

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