
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 \( x + y + z = 1 \) where \( x \geq 0 \), \( y \geq 0 \), \( z \geq 0 \), define \( f(z) = (z - x)(z - y) \). What is the range of values that \( f(z) \) can take?

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