
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 $\alpha$ and $\beta$ be the roots of $x^2 - 2px + p^2 - 1 = 0,$ and let $\gamma$ and $\delta$ be the roots of $x^2 - 2qx + q^2 - 1 = 0.$ Express
\[(\alpha - \gamma)(\beta - \delta)(\alpha - \delta)(\beta - \gamma)\] in terms of $p$ and $q.$

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