
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 $FGHIJ$, there is a vertical line of symmetry. The coordinates of vertices $F$, $G$, $H$, and $J$ are given as $F(0,0)$, $G(0,6)$, $H(3,t)$, and $J(6,0)$ respectively. What is the $y$-coordinate, $t$, of vertex $H$ so that the area of pentagon $FGHIJ$ is 60 square units?

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