
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
The non-negative numbers  $x,y,z$  satisfy the relation  $x + y+ z = 3$ . Find the smallest possible numerical value and the largest possible numerical value for the expression  $$ E(x,y, z) = \sqrt{x(y + 3)} + \sqrt{y(z + 3)} + \sqrt{z(x + 3)} . $$  

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