
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 the sets \( I = \{x \mid x \leqslant 8, x \in \mathbf{N}^{*} \} \), \( A \cup \complement_{I} B = \{1, 3, 4, 5, 6, 7\} \), \( \complement_{I} A \cup B = \{1, 2, 4, 5, 6, 8\} \), and \( \complement_{I} A \cap \complement_{I} B = \{1, 5, 6\} \), find sets \( A \) and \( B \).

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