
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 Immortal poses three two-digit numbers: \(a, b, c\). Ivan Tsarevich must provide him with three numbers: \(X, Y, Z\), after which Koschei will tell him the sum \(aX + bY + cZ\). Tsarevich must determine the numbers \(a, b,\) and \(c\), or he will be beheaded. What numbers should he state to survive?

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