
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
Let \( A = (0, 2), B = (3, 7), C = (7, 4), D = (9, 0) \). A quadrilateral is formed by connecting points \( A \) to \( B \), \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( A \). Calculate the perimeter of \( ABCD \) which can be expressed in the form \( a\sqrt{p} + b\sqrt{q} \) where \( a, b, p, q \) are integers. What is the sum of \( a \) and \( b \)?

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