
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
Let  $x$ ,  $y$ , and  $z$  be real numbers such that  $$ 12x - 9y^2 = 7 $$    $$ 6y - 9z^2 = -2 $$    $$ 12z - 9x^2 = 4 $$  Find  $6x^2 + 9y^2 + 12z^2$ .

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