
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
Positive  $x,y,z$  satisfy a system:  $\begin{cases}  x^2 + xy + y^2/3= 25 
 y^2/ 3  + z^2 = 9 
z^2 + zx + x^2 = 16 \end{cases}$ Find the value of  expression  $xy + 2yz + 3zx$ .

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