
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 $S=\{x|(x-1)(x-3)\geqslant 0\}$ and $T=\{x|x > 0\}$, determine the intersection $S\cap T$.

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