
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
On the plane are given  $ k\plus{}n$   distinct lines , where  $ k>1$  is integer and  $ n$  is integer as well.Any three of these lines do not pass through the

 same point . Among these lines exactly   $ k$  are parallel and all the other  $ n$  lines intersect each other.All  $ k\plus{}n$  lines define on the plane a partition 

of triangular , polygonic or not bounded regions. Two regions are colled different, if the have not common points 

or if they have common points only on their boundary.A regions is called ''good'' if it contained in a zone between two parallel lines .

If in a such given configuration the minimum number of ''good'' regionrs is  $ 176$  and the maximum number of these regions is  $ 221$ , find  $ k$  and  $ n$ .


Babis

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