
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
Graph  $G_1$  of a quadratic trinomial  $y = px^2 + qx + r$  with real coefficients intersects the graph  $G_2$  of a quadratic trinomial  $y = x^2$  in points  $A$ ,  $B$ . The intersection of tangents to  $G_2$  in points  $A$ ,  $B$  is point  $C$ . If  $C \in G_1$ , find all possible values of  $p$ . 

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