
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
Let's call a truncated circular right cone with the circumference of the lower base being 10 and the upper base being 9 a "mountain." The slope of the mountain is inclined at an angle of $60^{\circ}$ to the plane of the base. Point $A$ lies on the circumference of the lower base. A tourist begins to climb the slope from point $A$ to the nearest point of the upper base, then continues his journey along the edge of the upper base and travels a distance of 3. After that, he returns to point $A$ by the shortest route. What is the length of the return path?

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