
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
Consider the formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ which is $C = \frac{5}{9}(F - 30)$. An integer Fahrenheit temperature is converted to Celsius and rounded to the nearest integer, then converted back to Fahrenheit and again rounded to the nearest integer. Determine how many integer Fahrenheit temperatures between 30 and 800 inclusive results in the original temperature equaling the final temperature after these transformations.

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