
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
Find minimum of  $x+y+z$  where  $x$ ,  $y$  and  $z$  are real numbers such that  $x \geq 4$ ,  $y \geq 5$ ,  $z \geq 6$  and  $x^2+y^2+z^2 \geq 90$ 

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