
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
Determine the winning strategy for the modified version of the nim game, where the player forced to take the last stone loses. (It is enough to focus on the initial positions consisting of 3 heaps.)

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