
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
Pentagon $ABCDE$ has a vertical line of symmetry. The coordinates of $A$, $B$, $D$, and $E$ are given by $A(0,0)$, $B(0,6)$, $D(6,6)$, and $E(6,0)$ respectively. What is the $y$-coordinate of vertex $C$ so that the area of the pentagon is 72 square units?

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