
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
If positive real numbers  $x,y,z$  satisfy the following system of equations, compute  $x+y+z$ .  $$ xy+yz = 30 $$    $$ yz+zx = 36 $$    $$ zx+xy = 42 $$  *Proposed by Nathan Xiong*

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