
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 unicorn is tethered by a $25$-foot golden rope to the base of a magician's cylindrical tower whose radius is $10$ feet. The rope is attached to the tower at ground level and to the unicorn at a height of $5$ feet. The rope is pulled taut and the length of the rope touching the tower from its attachment at the ground to the point where it leaves the tower is $x$ feet. The unicorn can graze in a semicircle whose radius is determined by the segment of the rope from the point it stops touching the tower to the unicorn. Determine the length of the rope that touches the tower.

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