
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 real numbers  $x$ ,  $y$ , and  $z$  satisfy the system of equations  $$ x^2 + 27 = -8y + 10z $$    $$ y^2 + 196 = 18z + 13x $$    $$ z^2 + 119 = -3x + 30y $$  Find  $x + 3y + 5z$ .

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