
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
Koschei the Deathless poses a challenge with three two-digit numbers: \(a\), \(b\), and \(c\). Ivan Tsarevich must declare three numbers: \(X\), \(Y\), and \(Z\). Koschei will then inform him of the sum \(aX + bY + cZ\). Tsarevich must deduce the given numbers, or he will lose his head. How can he save himself?

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