
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
2009 cards, each with a blue side and a yellow side, are lined up blue side up on a table. Two players, situated on the same side of the table, take turns. A move consists of choosing a block of 50 cards where the leftmost card is blue and flipping all the cards in the block. The player who cannot move loses. Does the game necessarily end? If so, who has a winning strategy?

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