
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 \( x_{i} (i=1, 2, 3, 4) \) be real numbers such that \( \sum_{i=1}^{4} x_{i} = \sum_{i=1}^{4} x_{i}^{7} = 0 \). Find the value of the following expression: 
\[ u = x_{4} \left( x_{4} + x_{1} \right) \left( x_{4} + x_{2} \right) \left( x_{4} + x_{3} \right). \]

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