
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
A 50×50 chessboard is given, where each cell corresponds to a face of a die. The die rolls from the bottom-left corner of the board to the top-right corner. Each roll flips the die over one of its edges to an adjacent cell, and it is allowed to move only to the right or upward (movement to the left or downward is not permitted). Each cell of the board records the number of the die face that landed on it. What is the maximum possible sum of all the numbers recorded on the cells? What is the minimum possible sum?

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