
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 $E = (1, 3),$ $F = (3, 6),$ $G = (6, 3),$ and $H = (9, 1).$ A shape is formed by connecting $E$ to $F,$ $F$ to $G,$ $G$ to $H,$ and $H$ to $E.$ Calculate the perimeter of $EFGH,$ which can be expressed in the form $c\sqrt{p} + d\sqrt{q}$ where $c, d, p, q$ are integers. What is the sum of $c$ and $d$?

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