
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
In  $xyz$  plane find the volume of the solid formed by the points  $(x,\ y,\ z)$  satisfying the following system of inequalities.

\[0\leq z\leq 1+x+y-3(x-y)y,\ 0\leq y\leq 1,\ y\leq x\leq y+1.\]

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