
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
Given non-negative real numbers \( a, b, c, x, y, z \) that satisfy \( a+b+c = x+y+z = 1 \), find the maximum value of \( \left(a-x^{2}\right)\left(b-y^{2}\right)\left(c-z^{2}\right) \).

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