
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
The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ is $C = \frac{5}{9}(F-32)$. An integer Fahrenheit temperature is converted to Celsius using truncation (floor function), converted back to Fahrenheit using truncation, and again converted to Celsius using truncation.
For how many integer Fahrenheit temperatures between 30 and 1200 inclusive does the original temperature equal the final Fahrenheit temperature after two conversions?

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