
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
Let  $S = \{(x,y) | x = 1, 2, \ldots, 1993, y = 1, 2, 3, 4\}$ . If  $T \subset S$  and there aren't any squares in  $T.$  Find the maximum possible value of  $|T|.$  The squares in T use points in S as vertices.

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