
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 500 inclusive, does the original temperature, after conversion to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and rounded to the nearest integer once more, equal the original Fahrenheit temperature and also the final rounded Celsius temperature is greater than 10?

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