
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
Two players play alternately on a  $ 5 \times 5$  board. The first player always enters a  $ 1$  into an empty square and the second player always enters a  $ 0$  into an empty square. When the board is full, the sum of the numbers in each of the nine  $ 3 \times 3$  squares is calculated and the first player's score is the largest such sum. What is the largest score the first player can make, regardless of the responses of the second player?

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