
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 \( t \) be a positive number greater than zero.

Quadrilateral \(ABCD\) has vertices \(A(0,3), B(0,k), C(t, 10)\), and \(D(t, 0)\), where \(k>3\) and \(t>0\). The area of quadrilateral \(ABCD\) is 50 square units. What is the value of \(k\)?

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