
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 that \(a\), \(b\), and \(c\) are the side lengths of a triangle. If the positive real numbers \(x\), \(y\), and \(z\) satisfy \(x + y + z = 1\), find the maximum value of \(a x y + b y z + c z x\).

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