
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 universal set U=ℝ, the set $A=\{x\inℕ|lg(x-1)<1\}$, and the set $B=\{x|(x-3)(7-x)≥0\}$, calculate the set $A\cap UB$.

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