
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
What is the minimum number of cells that must be shaded in a square with a side length of 35 cells (a total of 1225 cells in the square) such that among any four cells forming an "L" shape, there is always at least one shaded cell?

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