
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
In the plane, there is a set of integer points \( S = \{ (a, b) \mid 1 \leqslant a, b \leqslant 5, a, b \in \mathbf{Z} \} \). Now consider a subset \( T \) of integer points in the plane such that for any point \( P \) in \( S \), there exists a distinct point \( Q \) in \( T \) such that the line segment \( PQ \) contains no other integer points except \( P \) and \( Q \). What is the minimum number of elements required in the set \( T \)?

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