
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
Let $A = \{x \in \mathbb{Z} \mid x \geq 10 \}$. Set $B$ is a subset of set $A$, and the elements in set $B$ satisfy the following conditions: ① The digits at each place of any element are all different; ② The sum of the digits at any two places of any element is not equal to 9.

(1) How many two-digit numbers and three-digit numbers are there in set $B$?

(2) Are there five-digit numbers in set $B$? Are there six-digit numbers?

(3) Arrange the elements in set $B$ from smallest to largest, and find the 1081st element.

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