
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 -100 and 100 inclusive does the original temperature equal the final temperature after converting it to Celsius, rounding to the nearest integer, converting back to Fahrenheit, and rounding to the nearest integer again?

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