
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 all real numbers \(a, b\) such that the inequality 
\[
xy + yz + zx \geqslant a(y^2 z^2 + z^2 x^2 + x^2 y^2) + bxyz
\]
holds for all non-negative \(x, y, z\) satisfying \(x + y + z = 1\).

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