
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 $C$ given by $C = \frac{5}{9}(F-32)$. An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer. Determine how many integer Fahrenheit temperatures between 50 and 2000 inclusive does the original temperature equal the final temperature?

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