
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
Tourists from the USA, when traveling to Europe, often use an approximate conversion formula to convert temperatures from degrees Celsius $C$ to degrees Fahrenheit $F$: $F = 2C + 30$. Indicate the range of temperatures (in degrees Celsius) for which the deviation of the temperature in degrees Fahrenheit obtained from the mentioned approximate formula from the temperature obtained from the exact formula does not exceed $5\%$. To obtain the exact formula, note that water freezes at $32^\circ F$ and boils at $212^\circ F$.

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