
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
If $p$, $q$, $r$, $s$, $t$, $u$, and $v$ are integers for which $1728x^4 + 64 = (px^3 + qx^2 + rx + s)(tx + u) + v$ for all $x$, then what is $p^2 + q^2 + r^2 + s^2 + t^2 + u^2 + v^2$?

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