
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
The isosceles triangle and the rectangle shown here have the same area in square units. If the length of the rectangle is $l$ and the breadth is $b$, with $l > b$, what is the height of the triangle, $h$, in terms of $l$ and $b$?

[asy]
draw((0,0)--(0,5)--(18,5)--(18,0)--cycle);
fill((0,0)--(18,7)--(0,10)--cycle,white);
draw((0,0)--(18,7)--(0,10)--cycle);
label("$l$",(9,5),N);
label("$h$",(9,7),N);
label("$b$",(18,2.5),E);
draw((0,5)--(18,5),dashed);
draw((0,7.5)--(0.5,7.5)--(0.5,7));
[/asy]

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