
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
Determine how many integer Fahrenheit temperatures between 50 and 2000 inclusive, when converted to Celsius (rounded to the nearest integer), converted back to Fahrenheit, and rounded again, result in the original Fahrenheit temperature.

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