
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
The following shows the graph of \( y = p x^{2} + 5 x + p \). The points \( A = (0, -2) \), \( B = \left(\frac{1}{2}, 0\right) \), \( C = (2, 0) \), and \( O = (0, 0) \) are given.

Find the value of \( p \).

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