
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
On the parabola  $y = x^2$  lie three different points  $P, Q$  and  $R$ . Their projections  $P', Q'$  and  $R'$  on the  $x$ -axis are equidistant and equal to  $s$  , i.e.  $| P'Q'| = | Q'R'| = s$ . Determine the area of  $\vartriangle PQR$  in terms of  $s$ 

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