
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 $(1,0)$, $(5,4)$, $(6,3)$, and $(6,0)$. Its perimeter can be expressed in the form $c\sqrt2+d\sqrt{17}$. Find the sum of $c$ and $d$.

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