
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 pentagon is formed by connecting the points $(0,0)$, $(2,0)$, $(3,2)$, $(2,3)$, and $(0,2)$, then returning to $(0,0)$. The perimeter of the pentagon can be written in the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{5}$, where $a$, $b$, $c$, and $d$ are whole numbers. Find $a+b+c+d$.

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