
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
Each vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. The vertices of the parallelogram are given as $(1,3)$, $(5,6)$, $(11,6)$, and $(7,3)$. What is the value of the sum $p + a$?

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