
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
The set  $S = \{ (a,b) \mid 1 \leq a, b \leq 5, a,b \in \mathbb{Z}\}$  be a set of points in the plane with integeral coordinates.  $T$  is another set of points with integeral coordinates in the plane. If for any point  $P \in S$ , there is always another point  $Q \in T$ ,  $P \neq Q$ , such that there is no other integeral points on segment  $PQ$ .  Find the least value of the number of elements of  $T$ .

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