
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
For all real numbers  $x,y,z$  such that  $-2\leq x,y,z \leq 2$  and  $x^2+y^2+z^2+xyz = 4$ , determine the least real number  $K$  satisfying \[\dfrac{z(xz+yz+y)}{xy+y^2+z^2+1} \leq K.\]

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