
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 hexagon is created by joining, in order, the points $(0,0)$, $(2,1)$, $(3,3)$, $(2,4)$, $(0,3)$, $(1,1)$, and back to $(0,0)$. The perimeter of this hexagon can be written in the form $p+q\sqrt{2}+r\sqrt{10}$, where $p$, $q$, and $r$ are integers. Find $p+q+r$.

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