
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 heptagon is formed by connecting sequentially the points \( (0,1), (1,3), (3,3), (4,2), (4,1), (3,0), (1,0), (0,1) \). Compute the perimeter of the heptagon, assuming it can be expressed in the form \( a + b\sqrt{2} + c\sqrt{3} + d\sqrt{5} + e\sqrt{10} \), where \( a, b, c, d, \) and \( e \) are integers. Find the sum \( a+b+c+d+e \).

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