
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
A quadrilateral has vertices at $(0,0)$, $(2,5)$, $(5,5)$, and $(6,2)$. Find its perimeter and express it in the form of $c\sqrt{p}+d\sqrt{q}$, where $c$, $d$, $p$, and $q$ are integers. Determine $c + d$.

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