
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
Given that \( x \), \( y \), and \( z \) are positive numbers, and they satisfy the following system of equations:
\[ 
\left\{\begin{array}{l}
x + y + xy = 8, \\
y + z + yz = 15, \\
z + x + zx = 35. 
\end{array}\right.
\]

Find the value of \( x + y + z + xy \).

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