
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
1) Anna and Bob are playing the following game: Anna starts, and in turn, they each place a cross in the squares of a $2013 \times 2013$ grid. The player who places the third cross in any $2 \times 2$ square loses. Which of the two players has a winning strategy?

2) What happens if they play with a $2014 \times 2014$ grid?

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