
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 bamboo pole's length is unknown. When the pole is placed horizontally in front of a door, it is 4 feet longer than the width of the door. When placed vertically, it is 2 feet taller than the height of the door. When placed diagonally, its length is exactly equal to the diagonal length of the door. How long is the bamboo pole?

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