
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
Consider the eighth-sphere \(\left\{(x, y, z) \mid x, y, z \geq 0, x^{2}+y^{2}+z^{2}=1\right\}\). What is the area of its projection onto the plane \(x+y+z=1\)?

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