
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 \( x, y, z \) satisfy the following equations:

\[ 4x^2 - 2x - 30yz = 25y^2 + 5y + 12xz = 9z^2 - 3z - 20xy. \]

Find all possible triples of numbers \( (a, b, c) \), where \( a = 2x + 5y \), \( b = 3z + 5y \), and \( c = 3z - 2x \).

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