
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
a) Seven convex polygons were cut out of cardboard and placed on a table in such a way that any six of them can be nailed to the table with two nails, but all seven cannot. Provide an example of such polygons and their arrangement. (The polygons may overlap.)

b) Eight convex polygons were cut out of cardboard and placed on a table in such a way that any seven of them can be nailed to the table with two nails, but all eight cannot. Provide an example of such polygons and their arrangement. (The polygons may overlap.)

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