
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 square has a perimeter of 40, and adjacent to it is a triangle with a height of 40. Both the square and the triangle share one side length in common. Determine the length of the base of the triangle, denoted as \( x \), given that the square and the triangle have the same area. [asy]
draw((0,0)--(2,0)--(2,2)--(0,2)--cycle);
draw((3,0)--(5,0)--(5,5)--cycle);
draw((4.8,0)--(4.8,0.2)--(5, 0.2));
label("$x$", (4,0), S);
label("40", (5, 2.5), E);
[/asy]

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