
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
**p1.** Is it possible to place six points in the plane and connect them by nonintersecting segments so that each point will be connected with exactly
a) Three other points?
b) Four other points?**p2.** Martian bank notes can have denomination of  $1, 3, 5, 25$  marts. Is it possible to change a note of  $25$  marts to exactly  $10$  notes of smaller denomination?**p3.** What is bigger: $99 \cdot 99  \cdot .... \cdot 99$  (product of  $20$  factors) or $9999  \cdot 9999  \cdot ...  \cdot 9999$  (product of  $10$  factors)?**p4.** How many whole numbers, from  $1$  to  $2006$ , are divisible neither by  $5$  nor by  $7$ ?


PS. You should use hide for answers.

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