
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
A rectangle and an isosceles triangle drawn on a plane share the same area. The rectangle has dimensions $a$ units and $b$ units for its length and width respectively. The base of the triangle is along one side of length $a$ of the rectangle. What is the height $h'$ of the triangle in terms of the rectangle's dimensions $a$ and $b$?

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