
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
There are 500 matches on the table. Two players take turns. On each turn, a player can take $1, 2, 4, 8, \ldots$ (any power of two) matches from the table. The player who cannot make a move loses.

Who wins with optimal play: the starting player or their partner?

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