
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
We rolled a truncated cone-shaped glass around a circular table in such a way that it never reached the edge of the table during its movement. The diameter of the table is $1.6 \mathrm{~m}$. The diameter of the bottom of the glass is $5 \mathrm{~cm}$, and the diameter of the top is $6.5 \mathrm{~cm}$. How tall can the glass be?

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