
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
The diagram shows a \(10 \times 9\) board with seven \(2 \times 1\) tiles already in place. What is the largest number of additional \(2 \times 1\) tiles that can be placed on the board, so that each tile covers exactly two \(1 \times 1\) cells of the board, and no tiles overlap?

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