
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
Among the coordinates  $(x,y)$   $(1\leq x,y\leq 101)$ , choose some points such that there does not exist  $4$  points which form a isoceles trapezium with its base parallel to either the  $x$  or  $y$  axis(including rectangles). Find the maximum number of coordinate points that can be chosen.

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