
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
For non-negative real numbers \( x_{1}, x_{2}, \cdots, x_{n} \) that satisfy the condition \( x_{1} + x_{2} + \cdots + x_{n} = 1 \), find the maximum value of \( \sum_{j=1}^{n} \left( x_{j}^{4} - x_{j}^{5} \right) \).

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