
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
Given sets $A=\{x|1<\log_{2}x<3, x\in \mathbb{N}^{*}\}$ and $B=\{x||x-6|<3, x\in \mathbb{N}^{*}\}$, answer the following questions:  
(1) How many different points can be obtained by taking one element from set A and one from set B to form coordinates in the Cartesian coordinate system?  
(2) How many different three-digit numbers, with digits increasing from left to right, can be formed by taking three different elements from $A \cup B$?  
(3) How many different natural numbers greater than 4000 can be formed by taking one element from set A and three elements from set B, with no repeated digits?

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