
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 combination \( (x, y, z) \) of three natural numbers, ranging from 10 to 20 inclusive, is a valid combination for the code lock if

\[ 3x^2 - y^2 - 7z = 99. \]

Find all valid combinations.

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