
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 ladybird is free to fly between the \(1 \times 1\) cells of a \(10 \times 10\) square grid. She may begin in any \(1 \times 1\) cell of the grid. Every second she flies to a different \(1 \times 1\) cell that she has not visited before. Find the smallest number of cells the ladybird must visit, including her starting cell, so that you can be certain that there is a \(2 \times 2\) grid of adjacent cells, each of which she has visited.

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