
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 $P=(1,2),$ $Q=(3,6),$ $R=(6,3),$ and $S=(8,1).$ A quadrilateral is formed by connecting $P$ to $Q$, $Q$ to $R$, $R$ to $S$, and $S$ to $P.$ Find the perimeter of $PQRS$, expressed in the form $c\sqrt{2}+d\sqrt{10}$, and find the sum $c+d$ where $c$ and $d$ are integers.

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