
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
Two players are playing the following game. There is a pile of stones. The first player on each of his turns takes 1 or 10 stones. The second player on each of his turns takes $m$ or $n$ stones. They take turns, starting with the first player. The player who cannot make a move loses. It is known that with any initial number of stones, the first player can always play in such a way to guarantee a win (regardless of how the second player plays). What can the values of $m$ and $n$ be?

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