
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
Below is a portion of the graph of a quadratic function, $y=p(x)=ax^2+bx+c$:
\[ \text{The graph has symmetry such that } p(10) = p(20) \text{ and } p(9) = p(21) \text{, etc., with an axis of symmetry at } x = 15. \]
Given that $p(25) = 9$ and the graph goes through the point $(0, 1)$, calculate $p(5)$.

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