
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
Points \((2, -3)\) and \((14, 9)\) are two opposite vertices of a parallelogram \(ABCD\). The other two vertices, \(C\) and \(D\), are positioned at \((5, 12)\) and \((11, -6)\) respectively. Calculate the coordinates of the point where the diagonals of the parallelogram intersect and find the area of the parallelogram.

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