
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
In a pentagon ABCDE, there is a vertical line of symmetry. Vertex E is moved to \(E(5,0)\), while \(A(0,0)\), \(B(0,5)\), and \(D(5,5)\). What is the \(y\)-coordinate of vertex C such that the area of pentagon ABCDE becomes 65 square units?

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