
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  $d$  be a positive number. On the parabola, whose equation has the coefficient  $1$  at the quadratic term, points  $A, B$  and  $C$  are chosen in such a way that the difference of the  $x$ -coordinates of points  $A$  and  $B$  is  $d$  and the difference of the  $x$ -coordinates of points  $B$  and  $C$  is also  $d$ . Find the area of the triangle  $ABC$ .

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