
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
Consider lattice points of a  $6*7$  grid.We start with two points  $A,B$ .We say two points  $X,Y$  connected if one can reflect several times WRT points  $A,B$  and reach from  $X$  to  $Y$ .Over all choices of  $A,B$  what is the minimum number of connected components?

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