
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

Let \(x_{1}, x_{2}, x_{3}, x_{4}\) be real numbers with \(x_{1} \neq x_{2}\). If \(\left(x_{1}+x_{3}\right)\left(x_{1}+x_{4}\right)=\left(x_{2}+x_{3}\right)\left(x_{2}+x_{4}\right)=n-10\) and \(p=\left(x_{1}+x_{3}\right)\left(x_{2}+x_{3}\right)+\left(x_{1}+x_{4}\right)\left(x_{2}+x_{4}\right)\), find the value of \(p\).

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