
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
Given that the length of the generatrix of a cone is $1$, and the radius of the base is $r$, if the area of the unfolded side surface of the cone is $\frac{1}{3}$ of the area of the circle where the sector is located, then $\frac{l}{r}=\_\_\_\_\_\_$.

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