
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
Each cell of a $10 \times 10$ board has a chip. You are allowed to select a diagonal that has an even number of chips and remove any chip from it.

What is the maximum number of chips that can be removed from the board using these operations?

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