
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 vectors $a=(x,-1)$, $b=(y-1,1)$, with $x$, $y\in(0,+\infty)$, if $a\parallel b$, find the minimum value of $t=x+\dfrac{1}{x}+y+\dfrac{1}{y}$.

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