
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 mathematical work "The Precious Mirror of Arithmetic" from the Ming Dynasty in China, there is a problem recorded as follows: "There is a hall with an unknown height and width. When a long rod is placed horizontally across the hall, the width of the door is four feet less than the length of the rod. When the rod is placed vertically, the length of the rod is two feet more than the height of the door. If the rod is diagonally placed through the hall, the corners fit exactly. Please calculate the height, width of the door, and the length of the rod." If the length of the rod is denoted as $x$ feet, the equation can be written as ______.

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