
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 *T-tetromino* is formed by adjoining three unit squares to form a  $1 \times 3$  rectangle, and adjoining on top of the middle square a fourth unit square.
Determine the least number of unit squares that must be removed from a  $202 \times 202$  grid so that it can be tiled using T-tetrominoes.

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