
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
Inside an angle of $90^{\circ}$, there is a given point located at distances of 8 and 1 from the sides of the angle. What is the minimum length of the segment passing through this point, whose ends lie on the sides of the angle?

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