
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 has its sides with lengths $a$ and $b$. A right triangle is constructed outside this rectangle such that one of its legs lies along the longer side of the rectangle and the other leg perpendicular to this side. If the area of the triangle is the same as the area of the rectangle, find the length of the altitude of the triangle to the hypotenuse.

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