
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 points $P=(1,2)$, $Q=(3,6)$, $R=(6,3)$, and $S=(8,1)$ form a quadrilateral $PQRS$. Find the perimeter of $PQRS$ and express it in the form $a\sqrt{p} + b\sqrt{q}$ where $a$, $b$, $p$, and $q$ are integers. What is the sum of $a$ and $b$?

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