
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
Given a quadratic function $y=ax^{2}+bx+c\left(a\neq 0\right)$, where $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$ are real numbers. When $x=x_{1}$ and $x=x_{2}+x_{3}+x_{4}+x_{5}$ (where $x_{1}\neq x_{2}+x_{3}+x_{4}+x_{5}$), the function values are both $5$. When $x=x_{1}+x_{2}$, the function value is $p$, and when $x=x_{3}+x_{4}+x_{5}$, the function value is $q$. Find $p-q$.

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