
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 parallelogram has vertices with coordinates \((1, 2)\), \((4, 6)\), \((10, 6)\), and \((7, 2)\). Find the sum of the perimeter and the area of the parallelogram.

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