
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
Let  $S$  be the locus of all points  $(x,y)$  in the first quadrant such that  $\dfrac{x}{t}+\dfrac{y}{1-t}=1$  for some  $t$  with  $0<t<1$ .  Find the area of  $S$ .

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