
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 spider can reach a point on the floor of a cylindrical room, directly opposite from where it hangs on the ceiling, in two ways with equal distances:

1. It descends vertically and then continues along the diameter of the floor.
2. It travels along the curved surface of the cylinder. When the curved surface is unrolled flat, its path is a straight line.

Calculate the ratio of the height to the diameter of the cylinder.

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