
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
We will call a grid polygon remarkable if it is not a rectangle and if several copies of it can be assembled into a polygon similar to the original one. For example, the 3-cell L-shaped polygon is a remarkable polygon.

a) Invent a remarkable polygon consisting of four cells.

b) For which $n > 4$ does there exist a remarkable polygon with $n$ cells?

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