
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
This system of $n$ linear equations with $n$ unknowns has an interesting property - the coefficients form an arithmetic progression. Consider a system similar to:

\[6x + 9y = 12\]
\[15x + 18y = 21\]

Can you find the unique solution to this system?

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