
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
If the radius of the top base of a truncated cone is $5$, the radius of the bottom base is $R$, and a section (a plane parallel to the top and bottom bases and equidistant from them) divides the truncated cone into two parts with a ratio of side areas of $1:2$, then $R=\_\_\_\_\_\_.$

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