
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 $(0,1)$, $(5,4)$, $(4,3)$, and $(3,0)$. Calculate its perimeter, expressed in the form $a\sqrt2+b\sqrt{c}$, where $a$, $b$, and $c$ are integers. What is the sum of $a$ and $b$?

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