
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
Lizzie and Alex are playing a game on the whiteboard. Initially,  $n$  twos are written
on the board. On a player’s turn they must either 
       1. change any single positive number to 0, or
       2. subtract one from any positive number of positive numbers on the board.
The game ends once all numbers are 0, and the last player who made a move wins. If Lizzie
always plays first, find all  $n$  for which Lizzie has a winning strategy.

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