
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 functions $f(x)=x^2+2$ and $g(x)=4x-1$ both have domain set $A$, find the respective ranges $S$ and $T$ of $f(x)$ and $g(x)$.
(Ⅰ) If $A=[1,2]$, find $S \cap T$;
(Ⅱ) If $A=[1,m]$ where $m>1$ and $S=T$, find the value of the real number $m$.

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