
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 share the same base. The height of the rectangle, $r$, equals the height of the triangle, $h$. Both geometric shapes together cover the same area as a square with side length $s$. If the base, equal for both the rectangle and the triangle, is known to be $s$, what is the height $h$ of the triangle in terms of $s$?

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