
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 the diagram, a rectangle has a perimeter of $60$, and the triangle has a height of $30$. If the rectangle and the triangle have the same area, what is the value of $x$?
[asy]
draw((0,0)--(3,0)--(3,1.5)--(0,1.5)--cycle);
draw((4,0)--(7,0)--(7,3)--cycle);
draw((6.8,0)--(6.8,.2)--(7,.2));
label("$x$",(5.5,0),S);
label("30",(7,1.5),E);
[/asy]

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