
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
The coordinates of three vertices of a quadrilateral $A B C D$ are $A(0, 0)$, $B(6, -1)$, $C(7, 7)$. The sides that meet at the fourth vertex are 5 units long and the angle at this vertex is greater than $180^{\circ}$. What is the area of the quadrilateral? And how much does the area increase if we only change the angle mentioned to be less than $180^{\circ}$?

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