
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
In the book "Nine Chapters on the Mathematical Art," the following problem is presented: There is a door of unknown height and width, and a pole of unknown length. When the pole is placed horizontally, it extends 4 feet beyond the width of the door; when placed vertically, it extends 2 feet beyond the height of the door; when placed diagonally, the pole is exactly equal to the diagonal of the door. What are the height, width, and diagonal length of the door? In this problem, the height of the door is ______.

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