
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 obtained by joining, in order, the points \((0,0)\), \((1,2)\), \((3,3)\), \((4,1)\), \((2,0)\), and back to \((0,0)\). The perimeter of the pentagon can be written in the form \(a + b\sqrt{c} + d\sqrt{e}\), where \(a\), \(b\), \(c\), \(d\), and \(e\) are whole numbers. Find \(a+b+c+d+e\).

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