
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
Two corridors, each with a height and width of 1 meter, run perpendicular to each other on the first and second floors of a building. The ceiling and floor separating them have been removed to create a hole measuring 1 meter by 1 meter in the floor of one corridor and the ceiling of the other. What is the maximum length of a beam that can be passed from one corridor to the other through the hole? Assume the beam is a rigid segment of zero thickness. Additionally, the separating floor thickness is zero, meaning the floor of the upper corridor and the ceiling of the lower corridor are in the same plane.

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