
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 36. The rectangle and triangle have the same area. What is the value of \( x \)? Assume the length of the rectangle is 3 times the width.
\[ \text{Diagram:} \]
\[ \text{Rectangle (Not shown): A rectangle with one unknown side labeled as } x \]
\[ \text{Triangle (Not shown): A triangle with height 36 and base labeled as } x \]

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