
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
For how many integer Fahrenheit temperatures between -50 and 1000 inclusive does the original temperature, when converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer, equal the original temperature?

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