
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 \( x, y, z, w \) be real numbers satisfying the following conditions:
(1) \( x + y + z + w = 0 \);
(2) \( x^7 + y^7 + z^7 + w^7 = 0 \).

Find the value of \( w(w + x)(w + y)(w + z) \).

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