
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 midline of an isosceles trapezoid is equal to 5. It is known that a circle can be inscribed in the trapezoid.

The midline of the trapezoid divides it into two parts, the ratio of the areas of which is \(\frac{7}{13}\). Find the height of the trapezoid.

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