
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
Positive reals  $p$  and  $q$  are such that the graph of  $y = x^2 - 2px + q$  does not intersect the  $x$ -axis. Find  $q$  if there is a unique pair of points  $A, B$  on the graph with  $AB$  parallel to the  $x$ -axis and  $\angle AOB = \frac{\pi}{2}$ , where  $O$  is the origin.

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